Mirrors/overte
3
0
Fork 0
mirror of https://github.com/overte-org/overte.git synced 2025-06-18 20:40:38 +02:00
Code Issues Projects Releases Packages Wiki Activity Actions
overte/libraries/shared/src/GeometryUtil.cpp
daleglass ed4164b59e
Update libraries/shared/src/GeometryUtil.cpp 
Co-authored-by: David Rowe <david@ctrlaltstudio.com>
2020-09-24 22:17:16 +02:00

1840 lines
84 KiB
C++
Raw Blame History

//
// GeometryUtil.cpp
// libraries/shared/src
//
// Created by Andrzej Kapolka on 5/21/13.
// Copyright 2013 High Fidelity, Inc.
//
// Distributed under the Apache License, Version 2.0.
// See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html
//
#include "GeometryUtil.h"
#include <assert.h>
#include <cstring>
#include <cmath>
#include <bitset>
#include <complex>
#include <qmath.h>
#include <glm/gtx/quaternion.hpp>
#include "glm/gtc/matrix_transform.hpp"
#include "NumericalConstants.h"
#include "GLMHelpers.h"
#include "Plane.h"
glm::vec3 computeVectorFromPointToSegment(const glm::vec3& point, const glm::vec3& start, const glm::vec3& end) {
// compute the projection of the point vector onto the segment vector
glm::vec3 segmentVector = end - start;
float lengthSquared = glm::dot(segmentVector, segmentVector);
if (lengthSquared < EPSILON) {
return start - point; // start and end the same
}
float proj = glm::dot(point - start, segmentVector) / lengthSquared;
if (proj <= 0.0f) { // closest to the start
return start - point;
} else if (proj >= 1.0f) { // closest to the end
return end - point;
} else { // closest to the middle
return start + segmentVector*proj - point;
}
}
// Computes the penetration between a point and a sphere (centered at the origin)
// if point is inside sphere: returns true and stores the result in 'penetration'
// (the vector that would move the point outside the sphere)
// otherwise returns false
bool findSpherePenetration(const glm::vec3& point, const glm::vec3& defaultDirection, float sphereRadius,
glm::vec3& penetration) {
float vectorLength = glm::length(point);
if (vectorLength < EPSILON) {
penetration = defaultDirection * sphereRadius;
return true;
}
float distance = vectorLength - sphereRadius;
if (distance < 0.0f) {
penetration = point * (-distance / vectorLength);
return true;
}
return false;
}
bool findSpherePointPenetration(const glm::vec3& sphereCenter, float sphereRadius,
const glm::vec3& point, glm::vec3& penetration) {
return findSpherePenetration(point - sphereCenter, glm::vec3(0.0f, -1.0f, 0.0f), sphereRadius, penetration);
}
bool findPointSpherePenetration(const glm::vec3& point, const glm::vec3& sphereCenter,
float sphereRadius, glm::vec3& penetration) {
return findSpherePenetration(sphereCenter - point, glm::vec3(0.0f, -1.0f, 0.0f), sphereRadius, penetration);
}
bool findSphereSpherePenetration(const glm::vec3& firstCenter, float firstRadius,
const glm::vec3& secondCenter, float secondRadius, glm::vec3& penetration) {
return findSpherePointPenetration(firstCenter, firstRadius + secondRadius, secondCenter, penetration);
}
bool findSphereSegmentPenetration(const glm::vec3& sphereCenter, float sphereRadius,
const glm::vec3& segmentStart, const glm::vec3& segmentEnd, glm::vec3& penetration) {
return findSpherePenetration(computeVectorFromPointToSegment(sphereCenter, segmentStart, segmentEnd),
glm::vec3(0.0f, -1.0f, 0.0f), sphereRadius, penetration);
}
bool findSphereCapsulePenetration(const glm::vec3& sphereCenter, float sphereRadius, const glm::vec3& capsuleStart,
const glm::vec3& capsuleEnd, float capsuleRadius, glm::vec3& penetration) {
return findSphereSegmentPenetration(sphereCenter, sphereRadius + capsuleRadius,
capsuleStart, capsuleEnd, penetration);
}
bool findPointCapsuleConePenetration(const glm::vec3& point, const glm::vec3& capsuleStart,
const glm::vec3& capsuleEnd, float startRadius, float endRadius, glm::vec3& penetration) {
// compute the projection of the point vector onto the segment vector
glm::vec3 segmentVector = capsuleEnd - capsuleStart;
float lengthSquared = glm::dot(segmentVector, segmentVector);
if (lengthSquared < EPSILON) { // start and end the same
return findPointSpherePenetration(point, capsuleStart,
glm::max(startRadius, endRadius), penetration);
}
float proj = glm::dot(point - capsuleStart, segmentVector) / lengthSquared;
if (proj <= 0.0f) { // closest to the start
return findPointSpherePenetration(point, capsuleStart, startRadius, penetration);
} else if (proj >= 1.0f) { // closest to the end
return findPointSpherePenetration(point, capsuleEnd, endRadius, penetration);
} else { // closest to the middle
return findPointSpherePenetration(point, capsuleStart + segmentVector * proj,
glm::mix(startRadius, endRadius, proj), penetration);
}
}
bool findSphereCapsuleConePenetration(const glm::vec3& sphereCenter,
float sphereRadius, const glm::vec3& capsuleStart, const glm::vec3& capsuleEnd,
float startRadius, float endRadius, glm::vec3& penetration) {
return findPointCapsuleConePenetration(sphereCenter, capsuleStart, capsuleEnd,
startRadius + sphereRadius, endRadius + sphereRadius, penetration);
}
bool findSpherePlanePenetration(const glm::vec3& sphereCenter, float sphereRadius,
const glm::vec4& plane, glm::vec3& penetration) {
float distance = glm::dot(plane, glm::vec4(sphereCenter, 1.0f)) - sphereRadius;
if (distance < 0.0f) {
penetration = glm::vec3(plane) * distance;
return true;
}
return false;
}
bool findSphereDiskPenetration(const glm::vec3& sphereCenter, float sphereRadius,
const glm::vec3& diskCenter, float diskRadius, float diskThickness, const glm::vec3& diskNormal,
glm::vec3& penetration) {
glm::vec3 localCenter = sphereCenter - diskCenter;
float axialDistance = glm::dot(localCenter, diskNormal);
if (std::fabs(axialDistance) < (sphereRadius + 0.5f * diskThickness)) {
// sphere hit the plane, but does it hit the disk?
// Note: this algorithm ignores edge hits.
glm::vec3 axialOffset = axialDistance * diskNormal;
if (glm::length(localCenter - axialOffset) < diskRadius) {
// yes, hit the disk
penetration = (std::fabs(axialDistance) - (sphereRadius + 0.5f * diskThickness) ) * diskNormal;
if (axialDistance < 0.0f) {
// hit the backside of the disk, so negate penetration vector
penetration *= -1.0f;
}
return true;
}
}
return false;
}
bool findCapsuleSpherePenetration(const glm::vec3& capsuleStart, const glm::vec3& capsuleEnd, float capsuleRadius,
const glm::vec3& sphereCenter, float sphereRadius, glm::vec3& penetration) {
if (findSphereCapsulePenetration(sphereCenter, sphereRadius,
capsuleStart, capsuleEnd, capsuleRadius, penetration)) {
penetration = -penetration;
return true;
}
return false;
}
bool findCapsulePlanePenetration(const glm::vec3& capsuleStart, const glm::vec3& capsuleEnd, float capsuleRadius,
const glm::vec4& plane, glm::vec3& penetration) {
float distance = glm::min(glm::dot(plane, glm::vec4(capsuleStart, 1.0f)),
glm::dot(plane, glm::vec4(capsuleEnd, 1.0f))) - capsuleRadius;
if (distance < 0.0f) {
penetration = glm::vec3(plane) * distance;
return true;
}
return false;
}
glm::vec3 addPenetrations(const glm::vec3& currentPenetration, const glm::vec3& newPenetration) {
// find the component of the new penetration in the direction of the current
float currentLength = glm::length(currentPenetration);
if (currentLength == 0.0f) {
return newPenetration;
}
glm::vec3 currentDirection = currentPenetration / currentLength;
float directionalComponent = glm::dot(newPenetration, currentDirection);
// if orthogonal or in the opposite direction, we can simply add
if (directionalComponent <= 0.0f) {
return currentPenetration + newPenetration;
}
// otherwise, we need to take the maximum component of current and new
return currentDirection * glm::max(directionalComponent, currentLength) +
newPenetration - (currentDirection * directionalComponent);
}
// finds the intersection between a ray and the facing plane on one axis
bool findIntersection(float origin, float direction, float corner, float size, float& distance) {
if (direction > EPSILON) {
distance = (corner - origin) / direction;
return true;
} else if (direction < -EPSILON) {
distance = (corner + size - origin) / direction;
return true;
}
return false;
}
// finds the intersection between a ray and the inside facing plane on one axis
bool findInsideOutIntersection(float origin, float direction, float corner, float size, float& distance) {
if (direction > EPSILON) {
distance = -1.0f * (origin - (corner + size)) / direction;
return true;
} else if (direction < -EPSILON) {
distance = -1.0f * (origin - corner) / direction;
return true;
}
return false;
}
// https://tavianator.com/fast-branchless-raybounding-box-intersections/
bool findRayAABoxIntersection(const glm::vec3& origin, const glm::vec3& direction, const glm::vec3& invDirection,
const glm::vec3& corner, const glm::vec3& scale, float& distance, BoxFace& face, glm::vec3& surfaceNormal) {
float t1, t2, newTmin, newTmax, tmin = -INFINITY, tmax = INFINITY;
int minAxis = -1, maxAxis = -1;
for (int i = 0; i < 3; ++i) {
t1 = (corner[i] - origin[i]) * invDirection[i];
t2 = (corner[i] + scale[i] - origin[i]) * invDirection[i];
newTmin = glm::min(t1, t2);
newTmax = glm::max(t1, t2);
minAxis = newTmin > tmin ? i : minAxis;
tmin = glm::max(tmin, newTmin);
maxAxis = newTmax < tmax ? i : maxAxis;
tmax = glm::min(tmax, newTmax);
}
if (tmax >= glm::max(tmin, 0.0f)) {
if (tmin < 0.0f) {
distance = tmax;
bool positiveDirection = direction[maxAxis] > 0.0f;
surfaceNormal = glm::vec3(0.0f);
surfaceNormal[maxAxis] = positiveDirection ? -1.0f : 1.0f;
face = positiveDirection ? BoxFace(2 * maxAxis + 1) : BoxFace(2 * maxAxis);
} else {
distance = tmin;
bool positiveDirection = direction[minAxis] > 0.0f;
surfaceNormal = glm::vec3(0.0f);
surfaceNormal[minAxis] = positiveDirection ? -1.0f : 1.0f;
face = positiveDirection ? BoxFace(2 * minAxis) : BoxFace(2 * minAxis + 1);
}
return true;
}
return false;
}
bool findRaySphereIntersection(const glm::vec3& origin, const glm::vec3& direction,
const glm::vec3& center, float radius, float& distance) {
glm::vec3 relativeOrigin = origin - center;
float c = glm::dot(relativeOrigin, relativeOrigin) - radius * radius;
if (c < 0.0f) {
distance = 0.0f;
return true; // starts inside the sphere
}
float b = 2.0f * glm::dot(direction, relativeOrigin);
float a = glm::dot(direction, direction);
float radicand = b * b - 4.0f * a * c;
if (radicand < 0.0f) {
return false; // doesn't hit the sphere
}
float t = 0.5f * (-b - sqrtf(radicand)) / a;
if (t < 0.0f) {
return false; // doesn't hit the sphere
}
distance = t;
return true;
}
bool pointInSphere(const glm::vec3& origin, const glm::vec3& center, float radius) {
glm::vec3 relativeOrigin = origin - center;
float c = glm::dot(relativeOrigin, relativeOrigin) - radius * radius;
return c <= 0.0f;
}
bool pointInCapsule(const glm::vec3& origin, const glm::vec3& start, const glm::vec3& end, float radius) {
glm::vec3 relativeOrigin = origin - start;
glm::vec3 relativeEnd = end - start;
float capsuleLength = glm::length(relativeEnd);
relativeEnd /= capsuleLength;
float originProjection = glm::dot(relativeEnd, relativeOrigin);
glm::vec3 constant = relativeOrigin - relativeEnd * originProjection;
float c = glm::dot(constant, constant) - radius * radius;
if (c < 0.0f) { // starts inside cylinder
if (originProjection < 0.0f) { // below start
return pointInSphere(origin, start, radius);
} else if (originProjection > capsuleLength) { // above end
return pointInSphere(origin, end, radius);
} else { // between start and end
return true;
}
}
return false;
}
bool findRayCapsuleIntersection(const glm::vec3& origin, const glm::vec3& direction,
const glm::vec3& start, const glm::vec3& end, float radius, float& distance) {
if (start == end) {
return findRaySphereIntersection(origin, direction, start, radius, distance); // handle degenerate case
}
glm::vec3 relativeOrigin = origin - start;
glm::vec3 relativeEnd = end - start;
float capsuleLength = glm::length(relativeEnd);
relativeEnd /= capsuleLength;
float originProjection = glm::dot(relativeEnd, relativeOrigin);
glm::vec3 constant = relativeOrigin - relativeEnd * originProjection;
float c = glm::dot(constant, constant) - radius * radius;
if (c < 0.0f) { // starts inside cylinder
if (originProjection < 0.0f) { // below start
return findRaySphereIntersection(origin, direction, start, radius, distance);
} else if (originProjection > capsuleLength) { // above end
return findRaySphereIntersection(origin, direction, end, radius, distance);
} else { // between start and end
distance = 0.0f;
return true;
}
}
glm::vec3 coefficient = direction - relativeEnd * glm::dot(relativeEnd, direction);
float a = glm::dot(coefficient, coefficient);
if (a == 0.0f) {
return false; // parallel to enclosing cylinder
}
float b = 2.0f * glm::dot(constant, coefficient);
float radicand = b * b - 4.0f * a * c;
if (radicand < 0.0f) {
return false; // doesn't hit the enclosing cylinder
}
float t = (-b - sqrtf(radicand)) / (2.0f * a);
if (t < 0.0f) {
return false; // doesn't hit the enclosing cylinder
}
glm::vec3 intersection = relativeOrigin + direction * t;
float intersectionProjection = glm::dot(relativeEnd, intersection);
if (intersectionProjection < 0.0f) { // below start
return findRaySphereIntersection(origin, direction, start, radius, distance);
} else if (intersectionProjection > capsuleLength) { // above end
return findRaySphereIntersection(origin, direction, end, radius, distance);
}
distance = t; // between start and end
return true;
}
// reference https://www.opengl.org/wiki/Calculating_a_Surface_Normal
glm::vec3 Triangle::getNormal() const {
glm::vec3 edge1 = v1 - v0;
glm::vec3 edge2 = v2 - v0;
return glm::normalize(glm::cross(edge1, edge2));
}
float Triangle::getArea() const {
glm::vec3 edge1 = v1 - v0;
glm::vec3 edge2 = v2 - v0;
return 0.5f * glm::length(glm::cross(edge1, edge2));
}
Triangle Triangle::operator*(const glm::mat4& transform) const {
return {
glm::vec3(transform * glm::vec4(v0, 1.0f)),
glm::vec3(transform * glm::vec4(v1, 1.0f)),
glm::vec3(transform * glm::vec4(v2, 1.0f))
};
}
// https://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm
bool findRayTriangleIntersection(const glm::vec3& origin, const glm::vec3& direction,
const glm::vec3& v0, const glm::vec3& v1, const glm::vec3& v2, float& distance, bool allowBackface) {
glm::vec3 firstSide = v1 - v0;
glm::vec3 secondSide = v2 - v0;
glm::vec3 P = glm::cross(direction, secondSide);
float det = glm::dot(firstSide, P);
if (!allowBackface && det < EPSILON) {
return false;
} else if (fabsf(det) < EPSILON) {
return false;
}
float invDet = 1.0f / det;
glm::vec3 T = origin - v0;
float u = glm::dot(T, P) * invDet;
if (u < 0.0f || u > 1.0f) {
return false;
}
glm::vec3 Q = glm::cross(T, firstSide);
float v = glm::dot(direction, Q) * invDet;
if (v < 0.0f || u + v > 1.0f) {
return false;
}
float t = glm::dot(secondSide, Q) * invDet;
if (t > EPSILON) {
distance = t;
return true;
}
return false;
}
static void getTrianglePlaneIntersectionPoints(const glm::vec3 trianglePoints[3], const float pointPlaneDistances[3],
const int clippedPointIndex, const int keptPointIndices[2],
glm::vec3 points[2]) {
assert(clippedPointIndex >= 0 && clippedPointIndex < 3);
const auto& clippedPoint = trianglePoints[clippedPointIndex];
const float clippedPointPlaneDistance = pointPlaneDistances[clippedPointIndex];
for (auto i = 0; i < 2; i++) {
assert(keptPointIndices[i] >= 0 && keptPointIndices[i] < 3);
const auto& keptPoint = trianglePoints[keptPointIndices[i]];
const float keptPointPlaneDistance = pointPlaneDistances[keptPointIndices[i]];
auto intersectionEdgeRatio = clippedPointPlaneDistance / (clippedPointPlaneDistance - keptPointPlaneDistance);
points[i] = clippedPoint + (keptPoint - clippedPoint) * intersectionEdgeRatio;
}
}
int clipTriangleWithPlane(const Triangle& triangle, const Plane& plane, Triangle* clippedTriangles, int maxClippedTriangleCount) {
float pointDistanceToPlane[3];
std::bitset<3> arePointsClipped;
glm::vec3 triangleVertices[3] = { triangle.v0, triangle.v1, triangle.v2 };
int clippedTriangleCount = 0;
int i;
for (i = 0; i < 3; i++) {
pointDistanceToPlane[i] = plane.distance(triangleVertices[i]);
arePointsClipped.set(i, pointDistanceToPlane[i] < 0.0f);
}
switch (arePointsClipped.count()) {
case 0:
// Easy, the entire triangle is kept as is.
*clippedTriangles = triangle;
clippedTriangleCount = 1;
break;
case 1:
{
int clippedPointIndex = 2;
int keptPointIndices[2] = { 0, 1 };
glm::vec3 newVertices[2];
// Determine which point was clipped.
if (arePointsClipped.test(0)) {
clippedPointIndex = 0;
keptPointIndices[0] = 2;
} else if (arePointsClipped.test(1)) {
clippedPointIndex = 1;
keptPointIndices[1] = 2;
}
// We have a quad now, so we need to create two triangles.
getTrianglePlaneIntersectionPoints(triangleVertices, pointDistanceToPlane, clippedPointIndex, keptPointIndices, newVertices);
clippedTriangles->v0 = triangleVertices[keptPointIndices[0]];
clippedTriangles->v1 = triangleVertices[keptPointIndices[1]];
clippedTriangles->v2 = newVertices[1];
clippedTriangles++;
clippedTriangleCount++;
if (clippedTriangleCount < maxClippedTriangleCount) {
clippedTriangles->v0 = triangleVertices[keptPointIndices[0]];
clippedTriangles->v1 = newVertices[0];
clippedTriangles->v2 = newVertices[1];
clippedTriangles++;
clippedTriangleCount++;
}
}
break;
case 2:
{
int keptPointIndex = 2;
int clippedPointIndices[2] = { 0, 1 };
glm::vec3 newVertices[2];
// Determine which point was NOT clipped.
if (!arePointsClipped.test(0)) {
keptPointIndex = 0;
clippedPointIndices[0] = 2;
} else if (!arePointsClipped.test(1)) {
keptPointIndex = 1;
clippedPointIndices[1] = 2;
}
// We have a single triangle
getTrianglePlaneIntersectionPoints(triangleVertices, pointDistanceToPlane, keptPointIndex, clippedPointIndices, newVertices);
clippedTriangles->v0 = triangleVertices[keptPointIndex];
clippedTriangles->v1 = newVertices[0];
clippedTriangles->v2 = newVertices[1];
clippedTriangleCount = 1;
}
break;
default:
// Entire triangle is clipped.
break;
}
return clippedTriangleCount;
}
int clipTriangleWithPlanes(const Triangle& triangle, const Plane* planes, int planeCount, Triangle* clippedTriangles, int maxClippedTriangleCount) {
auto planesEnd = planes + planeCount;
int triangleCount = 1;
std::vector<Triangle> trianglesToTest;
assert(maxClippedTriangleCount > 0);
*clippedTriangles = triangle;
while (planes < planesEnd && triangleCount) {
int clippedSubTriangleCount;
trianglesToTest.clear();
trianglesToTest.insert(trianglesToTest.begin(), clippedTriangles, clippedTriangles + triangleCount);
triangleCount = 0;
for (const auto& triangleToTest : trianglesToTest) {
clippedSubTriangleCount = clipTriangleWithPlane(triangleToTest, *planes,
clippedTriangles + triangleCount, maxClippedTriangleCount - triangleCount);
triangleCount += clippedSubTriangleCount;
if (triangleCount >= maxClippedTriangleCount) {
return triangleCount;
}
}
++planes;
}
return triangleCount;
}
// Do line segments (r1p1.x, r1p1.y)--(r1p2.x, r1p2.y) and (r2p1.x, r2p1.y)--(r2p2.x, r2p2.y) intersect?
// from: http://ptspts.blogspot.com/2010/06/how-to-determine-if-two-line-segments.html
bool doLineSegmentsIntersect(glm::vec2 r1p1, glm::vec2 r1p2, glm::vec2 r2p1, glm::vec2 r2p2) {
int d1 = computeDirection(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p1.x, r1p1.y);
int d2 = computeDirection(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p2.x, r1p2.y);
int d3 = computeDirection(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p1.x, r2p1.y);
int d4 = computeDirection(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p2.x, r2p2.y);
return (((d1 > 0 && d2 < 0) || (d1 < 0 && d2 > 0)) &&
((d3 > 0 && d4 < 0) || (d3 < 0 && d4 > 0))) ||
(d1 == 0 && isOnSegment(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p1.x, r1p1.y)) ||
(d2 == 0 && isOnSegment(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p2.x, r1p2.y)) ||
(d3 == 0 && isOnSegment(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p1.x, r2p1.y)) ||
(d4 == 0 && isOnSegment(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p2.x, r2p2.y));
}
bool findClosestApproachOfLines(glm::vec3 p1, glm::vec3 d1, glm::vec3 p2, glm::vec3 d2,
// return values...
float& t1, float& t2) {
// https://math.stackexchange.com/questions/1993953/closest-points-between-two-lines/1993990#1993990
// https://en.wikipedia.org/wiki/Skew_lines#Nearest_Points
glm::vec3 n1 = glm::cross(d1, glm::cross(d2, d1));
glm::vec3 n2 = glm::cross(d2, glm::cross(d1, d2));
float denom1 = glm::dot(d1, n2);
float denom2 = glm::dot(d2, n1);
if (denom1 != 0.0f && denom2 != 0.0f) {
t1 = glm::dot((p2 - p1), n2) / denom1;
t2 = glm::dot((p1 - p2), n1) / denom2;
return true;
} else {
t1 = 0.0f;
t2 = 0.0f;
return false;
}
}
bool isOnSegment(float xi, float yi, float xj, float yj, float xk, float yk) {
return (xi <= xk || xj <= xk) && (xk <= xi || xk <= xj) &&
(yi <= yk || yj <= yk) && (yk <= yi || yk <= yj);
}
int computeDirection(float xi, float yi, float xj, float yj, float xk, float yk) {
float a = (xk - xi) * (yj - yi);
float b = (xj - xi) * (yk - yi);
return a < b ? -1 : a > b ? 1 : 0;
}
//
// Polygon Clipping routines inspired by, pseudo code found here: http://www.cs.rit.edu/~icss571/clipTrans/PolyClipBack.html
//
// Coverage Map's polygon coordinates are from -1 to 1 in the following mapping to screen space.
//
// (0,0) (windowWidth, 0)
// -1,1 1,1
// +-----------------------+
// | | |
// | | |
// | -1,0 | |
// |-----------+-----------|
// | 0,0 |
// | | |
// | | |
// | | |
// +-----------------------+
// -1,-1 1,-1
// (0,windowHeight) (windowWidth,windowHeight)
//
const float PolygonClip::TOP_OF_CLIPPING_WINDOW = 1.0f;
const float PolygonClip::BOTTOM_OF_CLIPPING_WINDOW = -1.0f;
const float PolygonClip::LEFT_OF_CLIPPING_WINDOW = -1.0f;
const float PolygonClip::RIGHT_OF_CLIPPING_WINDOW = 1.0f;
const glm::vec2 PolygonClip::TOP_LEFT_CLIPPING_WINDOW ( LEFT_OF_CLIPPING_WINDOW , TOP_OF_CLIPPING_WINDOW );
const glm::vec2 PolygonClip::TOP_RIGHT_CLIPPING_WINDOW ( RIGHT_OF_CLIPPING_WINDOW, TOP_OF_CLIPPING_WINDOW );
const glm::vec2 PolygonClip::BOTTOM_LEFT_CLIPPING_WINDOW ( LEFT_OF_CLIPPING_WINDOW , BOTTOM_OF_CLIPPING_WINDOW );
const glm::vec2 PolygonClip::BOTTOM_RIGHT_CLIPPING_WINDOW ( RIGHT_OF_CLIPPING_WINDOW, BOTTOM_OF_CLIPPING_WINDOW );
void PolygonClip::clipToScreen(const glm::vec2* inputVertexArray, int inLength, glm::vec2*& outputVertexArray, int& outLength) {
int tempLengthA = inLength;
int tempLengthB;
int maxLength = inLength * 2;
glm::vec2* tempVertexArrayA = new glm::vec2[maxLength];
glm::vec2* tempVertexArrayB = new glm::vec2[maxLength];
// set up our temporary arrays
for (int i=0; i<inLength; i++) {
tempVertexArrayA[i] = inputVertexArray[i];
}
// Left edge
LineSegment2 edge;
edge[0] = TOP_LEFT_CLIPPING_WINDOW;
edge[1] = BOTTOM_LEFT_CLIPPING_WINDOW;
// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
// clean the array from tempVertexArrayA and copy cleaned result to tempVertexArrayA
copyCleanArray(tempLengthA, tempVertexArrayA, tempLengthB, tempVertexArrayB);
// Bottom Edge
edge[0] = BOTTOM_LEFT_CLIPPING_WINDOW;
edge[1] = BOTTOM_RIGHT_CLIPPING_WINDOW;
// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
// clean the array from tempVertexArrayA and copy cleaned result to tempVertexArrayA
copyCleanArray(tempLengthA, tempVertexArrayA, tempLengthB, tempVertexArrayB);
// Right Edge
edge[0] = BOTTOM_RIGHT_CLIPPING_WINDOW;
edge[1] = TOP_RIGHT_CLIPPING_WINDOW;
// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
// clean the array from tempVertexArrayA and copy cleaned result to tempVertexArrayA
copyCleanArray(tempLengthA, tempVertexArrayA, tempLengthB, tempVertexArrayB);
// Top Edge
edge[0] = TOP_RIGHT_CLIPPING_WINDOW;
edge[1] = TOP_LEFT_CLIPPING_WINDOW;
// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
// clean the array from tempVertexArrayA and copy cleaned result to tempVertexArrayA
copyCleanArray(tempLengthA, tempVertexArrayA, tempLengthB, tempVertexArrayB);
// copy final output to outputVertexArray
outputVertexArray = tempVertexArrayA;
outLength = tempLengthA;
// cleanup our unused temporary buffer...
delete[] tempVertexArrayB;
// Note: we don't delete tempVertexArrayA, because that's the caller's responsibility
}
void PolygonClip::sutherlandHodgmanPolygonClip(glm::vec2* inVertexArray, glm::vec2* outVertexArray,
int inLength, int& outLength, const LineSegment2& clipBoundary) {
glm::vec2 start, end; // Start, end point of current polygon edge
glm::vec2 intersection; // Intersection point with a clip boundary
outLength = 0;
start = inVertexArray[inLength - 1]; // Start with the last vertex in inVertexArray
for (int j = 0; j < inLength; j++) {
end = inVertexArray[j]; // Now start and end correspond to the vertices
// Cases 1 and 4 - the endpoint is inside the boundary
if (pointInsideBoundary(end,clipBoundary)) {
// Case 1 - Both inside
if (pointInsideBoundary(start, clipBoundary)) {
appendPoint(end, outLength, outVertexArray);
} else { // Case 4 - end is inside, but start is outside
segmentIntersectsBoundary(start, end, clipBoundary, intersection);
appendPoint(intersection, outLength, outVertexArray);
appendPoint(end, outLength, outVertexArray);
}
} else { // Cases 2 and 3 - end is outside
if (pointInsideBoundary(start, clipBoundary)) {
// Cases 2 - start is inside, end is outside
segmentIntersectsBoundary(start, end, clipBoundary, intersection);
appendPoint(intersection, outLength, outVertexArray);
} else {
// Case 3 - both are outside, No action
}
}
start = end; // Advance to next pair of vertices
}
}
bool PolygonClip::pointInsideBoundary(const glm::vec2& testVertex, const LineSegment2& clipBoundary) {
// bottom edge
if (clipBoundary[1].x > clipBoundary[0].x) {
if (testVertex.y >= clipBoundary[0].y) {
return true;
}
}
// top edge
if (clipBoundary[1].x < clipBoundary[0].x) {
if (testVertex.y <= clipBoundary[0].y) {
return true;
}
}
// right edge
if (clipBoundary[1].y > clipBoundary[0].y) {
if (testVertex.x <= clipBoundary[1].x) {
return true;
}
}
// left edge
if (clipBoundary[1].y < clipBoundary[0].y) {
if (testVertex.x >= clipBoundary[1].x) {
return true;
}
}
return false;
}
void PolygonClip::segmentIntersectsBoundary(const glm::vec2& first, const glm::vec2& second,
const LineSegment2& clipBoundary, glm::vec2& intersection) {
// horizontal
if (clipBoundary[0].y==clipBoundary[1].y) {
intersection.y = clipBoundary[0].y;
intersection.x = first.x + (clipBoundary[0].y - first.y) * (second.x - first.x) / (second.y - first.y);
} else { // Vertical
intersection.x = clipBoundary[0].x;
intersection.y = first.y + (clipBoundary[0].x - first.x) * (second.y - first.y) / (second.x - first.x);
}
}
void PolygonClip::appendPoint(glm::vec2 newVertex, int& outLength, glm::vec2* outVertexArray) {
outVertexArray[outLength].x = newVertex.x;
outVertexArray[outLength].y = newVertex.y;
outLength++;
}
// The copyCleanArray() function sets the resulting polygon of the previous step up to be the input polygon for next step of the
// clipping algorithm. As the Sutherland-Hodgman algorithm is a polygon clipping algorithm, it does not handle line
// clipping very well. The modification so that lines may be clipped as well as polygons is included in this function.
// when completed vertexArrayA will be ready for output and/or next step of clipping
void PolygonClip::copyCleanArray(int& lengthA, glm::vec2* vertexArrayA, int& lengthB, glm::vec2* vertexArrayB) {
// Fix lines: they will come back with a length of 3, from an original of length of 2
if ((lengthA == 2) && (lengthB == 3)) {
// The first vertex should be copied as is.
vertexArrayA[0] = vertexArrayB[0];
// If the first two vertices of the "B" array are same, then collapse them down to be the 2nd vertex
if (vertexArrayB[0].x == vertexArrayB[1].x) {
vertexArrayA[1] = vertexArrayB[2];
} else {
// Otherwise the first vertex should be the same as third vertex
vertexArrayA[1] = vertexArrayB[1];
}
lengthA=2;
} else {
// for all other polygons, then just copy the vertexArrayB to vertextArrayA for next step
lengthA = lengthB;
for (int i = 0; i < lengthB; i++) {
vertexArrayA[i] = vertexArrayB[i];
}
}
}
bool findRayRectangleIntersection(const glm::vec3& origin, const glm::vec3& direction, const glm::quat& rotation,
const glm::vec3& position, const glm::vec2& dimensions, float& distance) {
const glm::vec3 UNROTATED_NORMAL(0.0f, 0.0f, -1.0f);
glm::vec3 normal = rotation * UNROTATED_NORMAL;
bool maybeIntersects = false;
float denominator = glm::dot(normal, direction);
glm::vec3 offset = origin - position;
float normDotOffset = glm::dot(offset, normal);
float d = 0.0f;
if (fabsf(denominator) < EPSILON) {
// line is perpendicular to plane
if (fabsf(normDotOffset) < EPSILON) {
// ray starts on the plane
maybeIntersects = true;
// compute distance to closest approach
d = - glm::dot(offset, direction); // distance to closest approach of center of rectangle
if (d < 0.0f) {
// ray points away from center of rectangle, so ray's start is the closest approach
d = 0.0f;
}
}
} else {
d = - normDotOffset / denominator;
if (d > 0.0f) {
// ray points toward plane
maybeIntersects = true;
}
}
if (maybeIntersects) {
glm::vec3 hitPosition = origin + (d * direction);
glm::vec3 localHitPosition = glm::inverse(rotation) * (hitPosition - position);
glm::vec2 halfDimensions = 0.5f * dimensions;
if (fabsf(localHitPosition.x) < halfDimensions.x && fabsf(localHitPosition.y) < halfDimensions.y) {
// only update distance on intersection
distance = d;
return true;
}
}
return false;
}
// determines whether a value is within the extents
bool isWithin(float value, float corner, float size) {
return value >= corner && value <= corner + size;
}
bool aaBoxContains(const glm::vec3& point, const glm::vec3& corner, const glm::vec3& scale) {
return isWithin(point.x, corner.x, scale.x) &&
isWithin(point.y, corner.y, scale.y) &&
isWithin(point.z, corner.z, scale.z);
}
void checkPossibleParabolicIntersectionWithZPlane(float t, float& minDistance,
const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration, const glm::vec2& corner, const glm::vec2& scale) {
if (t < minDistance && t > 0.0f &&
isWithin(origin.x + velocity.x * t + 0.5f * acceleration.x * t * t, corner.x, scale.x) &&
isWithin(origin.y + velocity.y * t + 0.5f * acceleration.y * t * t, corner.y, scale.y)) {
minDistance = t;
}
}
// Intersect with the plane z = 0 and make sure the intersection is within dimensions
bool findParabolaRectangleIntersection(const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,
const glm::vec2& dimensions, float& parabolicDistance) {
glm::vec2 localCorner = -0.5f * dimensions;
float minDistance = FLT_MAX;
if (fabsf(acceleration.z) < EPSILON) {
if (fabsf(velocity.z) > EPSILON) {
// Handle the degenerate case where we only have a line in the z-axis
float possibleDistance = -origin.z / velocity.z;
checkPossibleParabolicIntersectionWithZPlane(possibleDistance, minDistance, origin, velocity, acceleration, localCorner, dimensions);
}
} else {
float a = 0.5f * acceleration.z;
float b = velocity.z;
float c = origin.z;
glm::vec2 possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int i = 0; i < 2; i++) {
checkPossibleParabolicIntersectionWithZPlane(possibleDistances[i], minDistance, origin, velocity, acceleration, localCorner, dimensions);
}
}
}
if (minDistance < FLT_MAX) {
parabolicDistance = minDistance;
return true;
}
return false;
}
bool findParabolaSphereIntersection(const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,
const glm::vec3& center, float radius, float& parabolicDistance) {
glm::vec3 localCenter = center - origin;
float radiusSquared = radius * radius;
float accelerationLength = glm::length(acceleration);
float minDistance = FLT_MAX;
if (accelerationLength < EPSILON) {
// Handle the degenerate case where acceleration == (0, 0, 0)
glm::vec3 offset = origin - center;
float a = glm::dot(velocity, velocity);
float b = 2.0f * glm::dot(velocity, offset);
float c = glm::dot(offset, offset) - radius * radius;
glm::vec2 possibleDistances(FLT_MAX);
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int i = 0; i < 2; i++) {
if (possibleDistances[i] < minDistance && possibleDistances[i] > 0.0f) {
minDistance = possibleDistances[i];
}
}
}
} else {
glm::vec3 vectorOnPlane = velocity;
if (fabsf(glm::dot(glm::normalize(velocity), glm::normalize(acceleration))) > 1.0f - EPSILON) {
// Handle the degenerate case where velocity is parallel to acceleration
// We pick t = 1 and calculate a second point on the plane
vectorOnPlane = velocity + 0.5f * acceleration;
}
// Get the normal of the plane, the cross product of two vectors on the plane
glm::vec3 normal = glm::normalize(glm::cross(vectorOnPlane, acceleration));
// Project vector from plane to sphere center onto the normal
float distance = glm::dot(localCenter, normal);
// Exit early if the sphere doesn't intersect the plane defined by the parabola
if (fabsf(distance) > radius) {
return false;
}
glm::vec3 circleCenter = center - distance * normal;
float circleRadius = sqrtf(radiusSquared - distance * distance);
glm::vec3 q = glm::normalize(acceleration);
glm::vec3 p = glm::cross(normal, q);
float a1 = accelerationLength * 0.5f;
float b1 = glm::dot(velocity, q);
float c1 = glm::dot(origin - circleCenter, q);
float a2 = glm::dot(velocity, p);
float b2 = glm::dot(origin - circleCenter, p);
float a = a1 * a1;
float b = 2.0f * a1 * b1;
float c = 2.0f * a1 * c1 + b1 * b1 + a2 * a2;
float d = 2.0f * b1 * c1 + 2.0f * a2 * b2;
float e = c1 * c1 + b2 * b2 - circleRadius * circleRadius;
glm::vec4 possibleDistances(FLT_MAX);
if (computeRealQuarticRoots(a, b, c, d, e, possibleDistances)) {
for (int i = 0; i < 4; i++) {
if (possibleDistances[i] < minDistance && possibleDistances[i] > 0.0f) {
minDistance = possibleDistances[i];
}
}
}
}
if (minDistance < FLT_MAX) {
parabolicDistance = minDistance;
return true;
}
return false;
}
void checkPossibleParabolicIntersectionWithTriangle(float t, float& minDistance,
const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,
const glm::vec3& localVelocity, const glm::vec3& localAcceleration, const glm::vec3& normal,
const glm::vec3& v0, const glm::vec3& v1, const glm::vec3& v2, bool allowBackface) {
// Check if we're hitting the backface in the rotated coordinate space
float localIntersectionVelocityZ = localVelocity.z + localAcceleration.z * t;
if (!allowBackface && localIntersectionVelocityZ < 0.0f) {
return;
}
// Check that the point is within all three sides
glm::vec3 point = origin + velocity * t + 0.5f * acceleration * t * t;
if (t < minDistance && t > 0.0f &&
glm::dot(normal, glm::cross(point - v1, v0 - v1)) > 0.0f &&
glm::dot(normal, glm::cross(v2 - v1, point - v1)) > 0.0f &&
glm::dot(normal, glm::cross(point - v0, v2 - v0)) > 0.0f) {
minDistance = t;
}
}
bool findParabolaTriangleIntersection(const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,
const glm::vec3& v0, const glm::vec3& v1, const glm::vec3& v2, float& parabolicDistance, bool allowBackface) {
glm::vec3 normal = glm::normalize(glm::cross(v2 - v1, v0 - v1));
// We transform the parabola and triangle so that the triangle is in the plane z = 0, with v0 at the origin
glm::quat inverseRot;
// Note: OpenGL view matrix is already the inverse of our camera matrix
// if the direction is nearly aligned with the Y axis, then use the X axis for 'up'
const float MAX_ABS_Y_COMPONENT = 0.9999991f;
if (fabsf(normal.y) > MAX_ABS_Y_COMPONENT) {
inverseRot = glm::quat_cast(glm::lookAt(glm::vec3(0.0f), normal, Vectors::UNIT_X));
} else {
inverseRot = glm::quat_cast(glm::lookAt(glm::vec3(0.0f), normal, Vectors::UNIT_Y));
}
glm::vec3 localOrigin = inverseRot * (origin - v0);
glm::vec3 localVelocity = inverseRot * velocity;
glm::vec3 localAcceleration = inverseRot * acceleration;
float minDistance = FLT_MAX;
if (fabsf(localAcceleration.z) < EPSILON) {
if (fabsf(localVelocity.z) > EPSILON) {
float possibleDistance = -localOrigin.z / localVelocity.z;
checkPossibleParabolicIntersectionWithTriangle(possibleDistance, minDistance, origin, velocity, acceleration,
localVelocity, localAcceleration, normal, v0, v1, v2, allowBackface);
}
} else {
float a = 0.5f * localAcceleration.z;
float b = localVelocity.z;
float c = localOrigin.z;
glm::vec2 possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int i = 0; i < 2; i++) {
checkPossibleParabolicIntersectionWithTriangle(possibleDistances[i], minDistance, origin, velocity, acceleration,
localVelocity, localAcceleration, normal, v0, v1, v2, allowBackface);
}
}
}
if (minDistance < FLT_MAX) {
parabolicDistance = minDistance;
return true;
}
return false;
}
bool findParabolaCapsuleIntersection(const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,
const glm::vec3& start, const glm::vec3& end, float radius, const glm::quat& rotation, float& parabolicDistance) {
if (start == end) {
return findParabolaSphereIntersection(origin, velocity, acceleration, start, radius, parabolicDistance); // handle degenerate case
}
if (glm::distance2(origin, start) < radius * radius) { // inside start sphere
float startDistance;
bool intersectsStart = findParabolaSphereIntersection(origin, velocity, acceleration, start, radius, startDistance);
if (glm::distance2(origin, end) < radius * radius) { // also inside end sphere
float endDistance;
bool intersectsEnd = findParabolaSphereIntersection(origin, velocity, acceleration, end, radius, endDistance);
if (endDistance < startDistance) {
parabolicDistance = endDistance;
return intersectsEnd;
}
}
parabolicDistance = startDistance;
return intersectsStart;
} else if (glm::distance2(origin, end) < radius * radius) { // inside end sphere (and not start sphere)
return findParabolaSphereIntersection(origin, velocity, acceleration, end, radius, parabolicDistance);
}
// We are either inside the middle of the capsule or outside it completely
// Either way, we need to check all three parts of the capsule and find the closest intersection
glm::vec3 results(FLT_MAX);
findParabolaSphereIntersection(origin, velocity, acceleration, start, radius, results[0]);
findParabolaSphereIntersection(origin, velocity, acceleration, end, radius, results[1]);
// We rotate the infinite cylinder to be aligned with the y-axis and then cap the values at the end
glm::quat inverseRot = glm::inverse(rotation);
glm::vec3 localOrigin = inverseRot * (origin - start);
glm::vec3 localVelocity = inverseRot * velocity;
glm::vec3 localAcceleration = inverseRot * acceleration;
float capsuleLength = glm::length(end - start);
const float MIN_ACCELERATION_PRODUCT = 0.00001f;
if (fabsf(localAcceleration.x * localAcceleration.z) < MIN_ACCELERATION_PRODUCT) {
// Handle the degenerate case where we only have a line in the XZ plane
float a = localVelocity.x * localVelocity.x + localVelocity.z * localVelocity.z;
float b = 2.0f * (localVelocity.x * localOrigin.x + localVelocity.z * localOrigin.z);
float c = localOrigin.x * localOrigin.x + localOrigin.z * localOrigin.z - radius * radius;
glm::vec2 possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int i = 0; i < 2; i++) {
if (possibleDistances[i] < results[2] && possibleDistances[i] > 0.0f) {
float y = localOrigin.y + localVelocity.y * possibleDistances[i] + 0.5f * localAcceleration.y * possibleDistances[i] * possibleDistances[i];
if (y > 0.0f && y < capsuleLength) {
results[2] = possibleDistances[i];
}
}
}
}
} else {
float a = 0.25f * (localAcceleration.x * localAcceleration.x + localAcceleration.z * localAcceleration.z);
float b = localVelocity.x * localAcceleration.x + localVelocity.z * localAcceleration.z;
float c = localOrigin.x * localAcceleration.x + localOrigin.z * localAcceleration.z + localVelocity.x * localVelocity.x + localVelocity.z * localVelocity.z;
float d = 2.0f * (localOrigin.x * localVelocity.x + localOrigin.z * localVelocity.z);
float e = localOrigin.x * localOrigin.x + localOrigin.z * localOrigin.z - radius * radius;
glm::vec4 possibleDistances(FLT_MAX);
if (computeRealQuarticRoots(a, b, c, d, e, possibleDistances)) {
for (int i = 0; i < 4; i++) {
if (possibleDistances[i] < results[2] && possibleDistances[i] > 0.0f) {
float y = localOrigin.y + localVelocity.y * possibleDistances[i] + 0.5f * localAcceleration.y * possibleDistances[i] * possibleDistances[i];
if (y > 0.0f && y < capsuleLength) {
results[2] = possibleDistances[i];
}
}
}
}
}
float minDistance = FLT_MAX;
for (int i = 0; i < 3; i++) {
minDistance = glm::min(minDistance, results[i]);
}
parabolicDistance = minDistance;
return minDistance != FLT_MAX;
}
void checkPossibleParabolicIntersection(float t, int i, float& minDistance, const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,
const glm::vec3& corner, const glm::vec3& scale, bool& hit) {
if (t < minDistance && t > 0.0f &&
isWithin(origin[(i + 1) % 3] + velocity[(i + 1) % 3] * t + 0.5f * acceleration[(i + 1) % 3] * t * t, corner[(i + 1) % 3], scale[(i + 1) % 3]) &&
isWithin(origin[(i + 2) % 3] + velocity[(i + 2) % 3] * t + 0.5f * acceleration[(i + 2) % 3] * t * t, corner[(i + 2) % 3], scale[(i + 2) % 3])) {
minDistance = t;
hit = true;
}
}
inline float parabolaVelocityAtT(float velocity, float acceleration, float t) {
return velocity + acceleration * t;
}
bool findParabolaAABoxIntersection(const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,
const glm::vec3& corner, const glm::vec3& scale, float& parabolicDistance, BoxFace& face, glm::vec3& surfaceNormal) {
float minDistance = FLT_MAX;
BoxFace minFace = UNKNOWN_FACE;
glm::vec3 minNormal;
glm::vec2 possibleDistances;
float a, b, c;
// Solve the intersection for each face of the cube. As we go, keep track of the smallest, positive, real distance
// that is within the bounds of the other two dimensions
for (int i = 0; i < 3; i++) {
if (fabsf(acceleration[i]) < EPSILON) {
// Handle the degenerate case where we only have a line in this axis
if (origin[i] < corner[i]) {
{ // min
if (velocity[i] > 0.0f) {
float possibleDistance = (corner[i] - origin[i]) / velocity[i];
bool hit = false;
checkPossibleParabolicIntersection(possibleDistance, i, minDistance, origin, velocity, acceleration, corner, scale, hit);
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
} else if (origin[i] > corner[i] + scale[i]) {
{ // max
if (velocity[i] < 0.0f) {
float possibleDistance = (corner[i] + scale[i] - origin[i]) / velocity[i];
bool hit = false;
checkPossibleParabolicIntersection(possibleDistance, i, minDistance, origin, velocity, acceleration, corner, scale, hit);
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
} else {
{ // min
if (velocity[i] < 0.0f) {
float possibleDistance = (corner[i] - origin[i]) / velocity[i];
bool hit = false;
checkPossibleParabolicIntersection(possibleDistance, i, minDistance, origin, velocity, acceleration, corner, scale, hit);
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
{ // max
if (velocity[i] > 0.0f) {
float possibleDistance = (corner[i] + scale[i] - origin[i]) / velocity[i];
bool hit = false;
checkPossibleParabolicIntersection(possibleDistance, i, minDistance, origin, velocity, acceleration, corner, scale, hit);
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
}
} else {
a = 0.5f * acceleration[i];
b = velocity[i];
if (origin[i] < corner[i]) {
// If we're below corner, we have the following cases:
// - within bounds on other axes
// - if +velocity or +acceleration
// - can only hit MIN_FACE with -normal
// - else
// - if +acceleration
// - can only hit MIN_FACE with -normal
// - else if +velocity
// - can hit MIN_FACE with -normal iff velocity at intersection is +
// - else can hit MAX_FACE with +normal iff velocity at intersection is -
if (origin[(i + 1) % 3] > corner[(i + 1) % 3] && origin[(i + 1) % 3] < corner[(i + 1) % 3] + scale[(i + 1) % 3] &&
origin[(i + 2) % 3] > corner[(i + 2) % 3] && origin[(i + 2) % 3] < corner[(i + 2) % 3] + scale[(i + 2) % 3]) {
if (velocity[i] > 0.0f || acceleration[i] > 0.0f) {
{ // min
c = origin[i] - corner[i];
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
}
} else {
if (acceleration[i] > 0.0f) {
{ // min
c = origin[i] - corner[i];
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
} else if (velocity[i] > 0.0f) {
bool hit = false;
{ // min
c = origin[i] - corner[i];
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) > 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
if (!hit) { // max
c = origin[i] - (corner[i] + scale[i]);
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) < 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
}
}
} else if (origin[i] > corner[i] + scale[i]) {
// If we're above corner + scale, we have the following cases:
// - within bounds on other axes
// - if -velocity or -acceleration
// - can only hit MAX_FACE with +normal
// - else
// - if -acceleration
// - can only hit MAX_FACE with +normal
// - else if -velocity
// - can hit MAX_FACE with +normal iff velocity at intersection is -
// - else can hit MIN_FACE with -normal iff velocity at intersection is +
if (origin[(i + 1) % 3] > corner[(i + 1) % 3] && origin[(i + 1) % 3] < corner[(i + 1) % 3] + scale[(i + 1) % 3] &&
origin[(i + 2) % 3] > corner[(i + 2) % 3] && origin[(i + 2) % 3] < corner[(i + 2) % 3] + scale[(i + 2) % 3]) {
if (velocity[i] < 0.0f || acceleration[i] < 0.0f) {
{ // max
c = origin[i] - (corner[i] + scale[i]);
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
}
} else {
if (acceleration[i] < 0.0f) {
{ // max
c = origin[i] - (corner[i] + scale[i]);
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
} else if (velocity[i] < 0.0f) {
bool hit = false;
{ // max
c = origin[i] - (corner[i] + scale[i]);
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) < 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
if (!hit) { // min
c = origin[i] - corner[i];
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) > 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
}
}
} else {
// If we're between corner and corner + scale, we have the following cases:
// - within bounds on other axes
// - if -velocity and -acceleration
// - can only hit MIN_FACE with +normal
// - else if +velocity and +acceleration
// - can only hit MAX_FACE with -normal
// - else
// - can hit MIN_FACE with +normal iff velocity at intersection is -
// - can hit MAX_FACE with -normal iff velocity at intersection is +
// - else
// - if -velocity and +acceleration
// - can hit MIN_FACE with -normal iff velocity at intersection is +
// - else if +velocity and -acceleration
// - can hit MAX_FACE with +normal iff velocity at intersection is -
if (origin[(i + 1) % 3] > corner[(i + 1) % 3] && origin[(i + 1) % 3] < corner[(i + 1) % 3] + scale[(i + 1) % 3] &&
origin[(i + 2) % 3] > corner[(i + 2) % 3] && origin[(i + 2) % 3] < corner[(i + 2) % 3] + scale[(i + 2) % 3]) {
if (velocity[i] < 0.0f && acceleration[i] < 0.0f) {
{ // min
c = origin[i] - corner[i];
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
} else if (velocity[i] > 0.0f && acceleration[i] > 0.0f) {
{ // max
c = origin[i] - (corner[i] + scale[i]);
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
} else {
{ // min
c = origin[i] - corner[i];
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) < 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
{ // max
c = origin[i] - (corner[i] + scale[i]);
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) > 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
}
} else {
if (velocity[i] < 0.0f && acceleration[i] > 0.0f) {
{ // min
c = origin[i] - corner[i];
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) > 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i);
minNormal = glm::vec3(0.0f);
minNormal[i] = -1.0f;
}
}
}
} else if (velocity[i] > 0.0f && acceleration[i] < 0.0f) {
{ // max
c = origin[i] - (corner[i] + scale[i]);
possibleDistances = { FLT_MAX, FLT_MAX };
if (computeRealQuadraticRoots(a, b, c, possibleDistances)) {
bool hit = false;
for (int j = 0; j < 2; j++) {
if (parabolaVelocityAtT(velocity[i], acceleration[i], possibleDistances[j]) < 0.0f) {
checkPossibleParabolicIntersection(possibleDistances[j], i, minDistance, origin, velocity, acceleration, corner, scale, hit);
}
}
if (hit) {
minFace = BoxFace(2 * i + 1);
minNormal = glm::vec3(0.0f);
minNormal[i] = 1.0f;
}
}
}
}
}
}
}
}
if (minDistance < FLT_MAX) {
parabolicDistance = minDistance;
face = minFace;
surfaceNormal = minNormal;
return true;
}
return false;
}
void swingTwistDecomposition(const glm::quat& rotation,
const glm::vec3& direction,
glm::quat& swing,
glm::quat& twist) {
// direction MUST be normalized else the decomposition will be inaccurate
assert(fabsf(glm::length2(direction) - 1.0f) < 1.0e-4f);
// the twist part has an axis (imaginary component) that is parallel to direction argument
glm::vec3 axisOfRotation(rotation.x, rotation.y, rotation.z);
glm::vec3 twistImaginaryPart = glm::dot(direction, axisOfRotation) * direction;
// and a real component that is relatively proportional to rotation's real component
twist = glm::normalize(glm::quat(rotation.w, twistImaginaryPart.x, twistImaginaryPart.y, twistImaginaryPart.z));
// once twist is known we can solve for swing:
// rotation = swing * twist --> swing = rotation * invTwist
swing = rotation * glm::inverse(twist);
}
// calculate the minimum angle between a point and a sphere.
float coneSphereAngle(const glm::vec3& coneCenter, const glm::vec3& coneDirection, const glm::vec3& sphereCenter, float sphereRadius) {
glm::vec3 d = sphereCenter - coneCenter;
float dLen = glm::length(d);
// theta is the angle between the coneDirection normal and the center of the sphere.
float theta = acosf(glm::dot(d, coneDirection) / dLen);
// phi is the deflection angle from the center of the sphere to a point tangent to the sphere.
float phi = atanf(sphereRadius / dLen);
return glm::max(0.0f, theta - phi);
}
// given a set of points, compute a best fit plane that passes as close as possible through all the points.
// http://www.ilikebigbits.com/blog/2015/3/2/plane-from-points
bool findPlaneFromPoints(const glm::vec3* points, size_t numPoints, glm::vec3& planeNormalOut, glm::vec3& pointOnPlaneOut) {
if (numPoints < 3) {
return false;
}
glm::vec3 sum;
for (size_t i = 0; i < numPoints; i++) {
sum += points[i];
}
glm::vec3 centroid = sum * (1.0f / (float)numPoints);
float xx = 0.0f, xy = 0.0f, xz = 0.0f;
float yy = 0.0f, yz = 0.0f, zz = 0.0f;
for (size_t i = 0; i < numPoints; i++) {
glm::vec3 r = points[i] - centroid;
xx += r.x * r.x;
xy += r.x * r.y;
xz += r.x * r.z;
yy += r.y * r.y;
yz += r.y * r.z;
zz += r.z * r.z;
}
float det_x = yy * zz - yz * yz;
float det_y = xx * zz - xz * xz;
float det_z = xx * yy - xy * xy;
float det_max = std::max(std::max(det_x, det_y), det_z);
if (det_max == 0.0f) {
return false; // The points don't span a plane
}
glm::vec3 dir;
if (det_max == det_x) {
float a = (xz * yz - xy * zz) / det_x;
float b = (xy * yz - xz * yy) / det_x;
dir = glm::vec3(1.0f, a, b);
} else if (det_max == det_y) {
float a = (yz * xz - xy * zz) / det_y;
float b = (xy * xz - yz * xx) / det_y;
dir = glm::vec3(a, 1.0f, b);
} else {
float a = (yz * xy - xz * yy) / det_z;
float b = (xz * xy - yz * xx) / det_z;
dir = glm::vec3(a, b, 1.0f);
}
pointOnPlaneOut = centroid;
planeNormalOut = glm::normalize(dir);
return true;
}
bool findIntersectionOfThreePlanes(const glm::vec4& planeA, const glm::vec4& planeB, const glm::vec4& planeC, glm::vec3& intersectionPointOut) {
glm::vec3 normalA(planeA);
glm::vec3 normalB(planeB);
glm::vec3 normalC(planeC);
glm::vec3 u = glm::cross(normalB, normalC);
float denom = glm::dot(normalA, u);
if (fabsf(denom) < EPSILON) {
return false; // planes do not intersect in a point.
} else {
intersectionPointOut = (planeA.w * u + glm::cross(normalA, planeC.w * normalB - planeB.w * normalC)) / denom;
return true;
}
}
const float INV_SQRT_3 = 1.0f / sqrtf(3.0f);
const int DOP14_COUNT = 14;
const glm::vec3 DOP14_NORMALS[DOP14_COUNT] = {
Vectors::UNIT_X,
-Vectors::UNIT_X,
Vectors::UNIT_Y,
-Vectors::UNIT_Y,
Vectors::UNIT_Z,
-Vectors::UNIT_Z,
glm::vec3(INV_SQRT_3, INV_SQRT_3, INV_SQRT_3),
-glm::vec3(INV_SQRT_3, INV_SQRT_3, INV_SQRT_3),
glm::vec3(INV_SQRT_3, -INV_SQRT_3, INV_SQRT_3),
-glm::vec3(INV_SQRT_3, -INV_SQRT_3, INV_SQRT_3),
glm::vec3(INV_SQRT_3, INV_SQRT_3, -INV_SQRT_3),
-glm::vec3(INV_SQRT_3, INV_SQRT_3, -INV_SQRT_3),
glm::vec3(INV_SQRT_3, -INV_SQRT_3, -INV_SQRT_3),
-glm::vec3(INV_SQRT_3, -INV_SQRT_3, -INV_SQRT_3)
};
typedef std::tuple<int, int, int> Int3Tuple;
const std::tuple<int, int, int> DOP14_PLANE_COMBINATIONS[] = {
Int3Tuple(0, 2, 4), Int3Tuple(0, 2, 5), Int3Tuple(0, 2, 6), Int3Tuple(0, 2, 7), Int3Tuple(0, 2, 8), Int3Tuple(0, 2, 9), Int3Tuple(0, 2, 10), Int3Tuple(0, 2, 11), Int3Tuple(0, 2, 12), Int3Tuple(0, 2, 13),
Int3Tuple(0, 3, 4), Int3Tuple(0, 3, 5), Int3Tuple(0, 3, 6), Int3Tuple(0, 3, 7), Int3Tuple(0, 3, 8), Int3Tuple(0, 3, 9), Int3Tuple(0, 3, 10), Int3Tuple(0, 3, 11), Int3Tuple(0, 3, 12), Int3Tuple(0, 3, 13),
Int3Tuple(0, 4, 6), Int3Tuple(0, 4, 7), Int3Tuple(0, 4, 8), Int3Tuple(0, 4, 9), Int3Tuple(0, 4, 10), Int3Tuple(0, 4, 11), Int3Tuple(0, 4, 12), Int3Tuple(0, 4, 13),
Int3Tuple(0, 5, 6), Int3Tuple(0, 5, 7), Int3Tuple(0, 5, 8), Int3Tuple(0, 5, 9), Int3Tuple(0, 5, 10), Int3Tuple(0, 5, 11), Int3Tuple(0, 5, 12), Int3Tuple(0, 5, 13),
Int3Tuple(0, 6, 8), Int3Tuple(0, 6, 9), Int3Tuple(0, 6, 10), Int3Tuple(0, 6, 11), Int3Tuple(0, 6, 12), Int3Tuple(0, 6, 13),
Int3Tuple(0, 7, 8), Int3Tuple(0, 7, 9), Int3Tuple(0, 7, 10), Int3Tuple(0, 7, 11), Int3Tuple(0, 7, 12), Int3Tuple(0, 7, 13),
Int3Tuple(0, 8, 10), Int3Tuple(0, 8, 11), Int3Tuple(0, 8, 12), Int3Tuple(0, 8, 13), Int3Tuple(0, 9, 10),
Int3Tuple(0, 9, 11), Int3Tuple(0, 9, 12), Int3Tuple(0, 9, 13),
Int3Tuple(0, 10, 12), Int3Tuple(0, 10, 13),
Int3Tuple(0, 11, 12), Int3Tuple(0, 11, 13),
Int3Tuple(1, 2, 4), Int3Tuple(1, 2, 5), Int3Tuple(1, 2, 6), Int3Tuple(1, 2, 7), Int3Tuple(1, 2, 8), Int3Tuple(1, 2, 9), Int3Tuple(1, 2, 10), Int3Tuple(1, 2, 11), Int3Tuple(1, 2, 12), Int3Tuple(1, 2, 13),
Int3Tuple(1, 3, 4), Int3Tuple(1, 3, 5), Int3Tuple(1, 3, 6), Int3Tuple(1, 3, 7), Int3Tuple(1, 3, 8), Int3Tuple(1, 3, 9), Int3Tuple(1, 3, 10), Int3Tuple(1, 3, 11), Int3Tuple(1, 3, 12), Int3Tuple(1, 3, 13),
Int3Tuple(1, 4, 6), Int3Tuple(1, 4, 7), Int3Tuple(1, 4, 8), Int3Tuple(1, 4, 9), Int3Tuple(1, 4, 10), Int3Tuple(1, 4, 11), Int3Tuple(1, 4, 12), Int3Tuple(1, 4, 13),
Int3Tuple(1, 5, 6), Int3Tuple(1, 5, 7), Int3Tuple(1, 5, 8), Int3Tuple(1, 5, 9), Int3Tuple(1, 5, 10), Int3Tuple(1, 5, 11), Int3Tuple(1, 5, 12), Int3Tuple(1, 5, 13),
Int3Tuple(1, 6, 8), Int3Tuple(1, 6, 9), Int3Tuple(1, 6, 10), Int3Tuple(1, 6, 11), Int3Tuple(1, 6, 12), Int3Tuple(1, 6, 13),
Int3Tuple(1, 7, 8), Int3Tuple(1, 7, 9), Int3Tuple(1, 7, 10), Int3Tuple(1, 7, 11), Int3Tuple(1, 7, 12), Int3Tuple(1, 7, 13),
Int3Tuple(1, 8, 10), Int3Tuple(1, 8, 11), Int3Tuple(1, 8, 12), Int3Tuple(1, 8, 13),
Int3Tuple(1, 9, 10), Int3Tuple(1, 9, 11), Int3Tuple(1, 9, 12), Int3Tuple(1, 9, 13),
Int3Tuple(1, 10, 12), Int3Tuple(1, 10, 13),
Int3Tuple(1, 11, 12), Int3Tuple(1, 11, 13),
Int3Tuple(2, 4, 6), Int3Tuple(2, 4, 7), Int3Tuple(2, 4, 8), Int3Tuple(2, 4, 9), Int3Tuple(2, 4, 10), Int3Tuple(2, 4, 11), Int3Tuple(2, 4, 12), Int3Tuple(2, 4, 13),
Int3Tuple(2, 5, 6), Int3Tuple(2, 5, 7), Int3Tuple(2, 5, 8), Int3Tuple(2, 5, 9), Int3Tuple(2, 5, 10), Int3Tuple(2, 5, 11), Int3Tuple(2, 5, 12), Int3Tuple(2, 5, 13),
Int3Tuple(2, 6, 8), Int3Tuple(2, 6, 9), Int3Tuple(2, 6, 10), Int3Tuple(2, 6, 11), Int3Tuple(2, 6, 12), Int3Tuple(2, 6, 13),
Int3Tuple(2, 7, 8), Int3Tuple(2, 7, 9), Int3Tuple(2, 7, 10), Int3Tuple(2, 7, 11), Int3Tuple(2, 7, 12), Int3Tuple(2, 7, 13),
Int3Tuple(2, 8, 10), Int3Tuple(2, 8, 11), Int3Tuple(2, 8, 12), Int3Tuple(2, 8, 13),
Int3Tuple(2, 9, 10), Int3Tuple(2, 9, 11), Int3Tuple(2, 9, 12), Int3Tuple(2, 9, 13),
Int3Tuple(2, 10, 12), Int3Tuple(2, 10, 13),
Int3Tuple(2, 11, 12), Int3Tuple(2, 11, 13),
Int3Tuple(3, 4, 6), Int3Tuple(3, 4, 7), Int3Tuple(3, 4, 8), Int3Tuple(3, 4, 9), Int3Tuple(3, 4, 10), Int3Tuple(3, 4, 11), Int3Tuple(3, 4, 12), Int3Tuple(3, 4, 13),
Int3Tuple(3, 5, 6), Int3Tuple(3, 5, 7), Int3Tuple(3, 5, 8), Int3Tuple(3, 5, 9), Int3Tuple(3, 5, 10), Int3Tuple(3, 5, 11), Int3Tuple(3, 5, 12), Int3Tuple(3, 5, 13),
Int3Tuple(3, 6, 8), Int3Tuple(3, 6, 9), Int3Tuple(3, 6, 10), Int3Tuple(3, 6, 11), Int3Tuple(3, 6, 12), Int3Tuple(3, 6, 13),
Int3Tuple(3, 7, 8), Int3Tuple(3, 7, 9), Int3Tuple(3, 7, 10), Int3Tuple(3, 7, 11), Int3Tuple(3, 7, 12), Int3Tuple(3, 7, 13),
Int3Tuple(3, 8, 10), Int3Tuple(3, 8, 11), Int3Tuple(3, 8, 12), Int3Tuple(3, 8, 13),
Int3Tuple(3, 9, 10), Int3Tuple(3, 9, 11), Int3Tuple(3, 9, 12), Int3Tuple(3, 9, 13),
Int3Tuple(3, 10, 12), Int3Tuple(3, 10, 13),
Int3Tuple(3, 11, 12), Int3Tuple(3, 11, 13),
Int3Tuple(4, 6, 8), Int3Tuple(4, 6, 9), Int3Tuple(4, 6, 10), Int3Tuple(4, 6, 11), Int3Tuple(4, 6, 12), Int3Tuple(4, 6, 13),
Int3Tuple(4, 7, 8), Int3Tuple(4, 7, 9), Int3Tuple(4, 7, 10), Int3Tuple(4, 7, 11), Int3Tuple(4, 7, 12), Int3Tuple(4, 7, 13),
Int3Tuple(4, 8, 10), Int3Tuple(4, 8, 11), Int3Tuple(4, 8, 12), Int3Tuple(4, 8, 13),
Int3Tuple(4, 9, 10), Int3Tuple(4, 9, 11), Int3Tuple(4, 9, 12), Int3Tuple(4, 9, 13),
Int3Tuple(4, 10, 12), Int3Tuple(4, 10, 13),
Int3Tuple(4, 11, 12), Int3Tuple(4, 11, 13),
Int3Tuple(5, 6, 8), Int3Tuple(5, 6, 9), Int3Tuple(5, 6, 10), Int3Tuple(5, 6, 11), Int3Tuple(5, 6, 12), Int3Tuple(5, 6, 13),
Int3Tuple(5, 7, 8), Int3Tuple(5, 7, 9), Int3Tuple(5, 7, 10), Int3Tuple(5, 7, 11), Int3Tuple(5, 7, 12), Int3Tuple(5, 7, 13),
Int3Tuple(5, 8, 10), Int3Tuple(5, 8, 11), Int3Tuple(5, 8, 12), Int3Tuple(5, 8, 13),
Int3Tuple(5, 9, 10), Int3Tuple(5, 9, 11), Int3Tuple(5, 9, 12), Int3Tuple(5, 9, 13),
Int3Tuple(5, 10, 12), Int3Tuple(5, 10, 13),
Int3Tuple(5, 11, 12), Int3Tuple(5, 11, 13),
Int3Tuple(6, 8, 10), Int3Tuple(6, 8, 11), Int3Tuple(6, 8, 12), Int3Tuple(6, 8, 13),
Int3Tuple(6, 9, 10), Int3Tuple(6, 9, 11), Int3Tuple(6, 9, 12), Int3Tuple(6, 9, 13),
Int3Tuple(6, 10, 12), Int3Tuple(6, 10, 13),
Int3Tuple(6, 11, 12), Int3Tuple(6, 11, 13),
Int3Tuple(7, 8, 10), Int3Tuple(7, 8, 11), Int3Tuple(7, 8, 12), Int3Tuple(7, 8, 13),
Int3Tuple(7, 9, 10), Int3Tuple(7, 9, 11), Int3Tuple(7, 9, 12), Int3Tuple(7, 9, 13),
Int3Tuple(7, 10, 12), Int3Tuple(7, 10, 13),
Int3Tuple(7, 11, 12), Int3Tuple(7, 11, 13),
Int3Tuple(8, 10, 12), Int3Tuple(8, 10, 13),
Int3Tuple(8, 11, 12), Int3Tuple(8, 11, 13),
Int3Tuple(9, 10, 12), Int3Tuple(9, 10, 13),
Int3Tuple(9, 11, 12), Int3Tuple(9, 11, 13)
};
void generateBoundryLinesForDop14(const std::vector<float>& dots, const glm::vec3& center, std::vector<glm::vec3>& linesOut) {
if (dots.size() != DOP14_COUNT) {
return;
}
// iterate over all purmutations of non-parallel planes.
// find all the vertices that lie on the surface of the k-dop
std::vector<glm::vec3> vertices;
for (auto& tuple : DOP14_PLANE_COMBINATIONS) {
int i = std::get<0>(tuple);
int j = std::get<1>(tuple);
int k = std::get<2>(tuple);
glm::vec4 planeA(DOP14_NORMALS[i], dots[i]);
glm::vec4 planeB(DOP14_NORMALS[j], dots[j]);
glm::vec4 planeC(DOP14_NORMALS[k], dots[k]);
glm::vec3 intersectionPoint;
const float IN_FRONT_MARGIN = 0.01f;
if (findIntersectionOfThreePlanes(planeA, planeB, planeC, intersectionPoint)) {
bool inFront = false;
for (int p = 0; p < DOP14_COUNT; p++) {
if (glm::dot(DOP14_NORMALS[p], intersectionPoint) > dots[p] + IN_FRONT_MARGIN) {
inFront = true;
}
}
if (!inFront) {
vertices.push_back(intersectionPoint);
}
}
}
// build a set of lines between these vertices, that also lie on the surface of the k-dop.
for (size_t i = 0; i < vertices.size(); i++) {
for (size_t j = i; j < vertices.size(); j++) {
glm::vec3 midPoint = (vertices[i] + vertices[j]) * 0.5f;
int onSurfaceCount = 0;
const float SURFACE_MARGIN = 0.01f;
for (int p = 0; p < DOP14_COUNT; p++) {
float d = glm::dot(DOP14_NORMALS[p], midPoint);
if (d > dots[p] - SURFACE_MARGIN && d < dots[p] + SURFACE_MARGIN) {
onSurfaceCount++;
}
}
if (onSurfaceCount > 1) {
linesOut.push_back(vertices[i] + center);
linesOut.push_back(vertices[j] + center);
}
}
}
}
bool computeRealQuadraticRoots(float a, float b, float c, glm::vec2& roots) {
float discriminant = b * b - 4.0f * a * c;
if (discriminant < 0.0f) {
return false;
} else if (discriminant == 0.0f) {
roots.x = (-b + sqrtf(discriminant)) / (2.0f * a);
} else {
float discriminantRoot = sqrtf(discriminant);
roots.x = (-b + discriminantRoot) / (2.0f * a);
roots.y = (-b - discriminantRoot) / (2.0f * a);
}
return true;
}
// The following functions provide an analytical solution to a quartic equation, adapted from the solution here: https://github.com/sasamil/Quartic
unsigned int solveP3(float* x, float a, float b, float c) {
float a2 = a * a;
float q = (a2 - 3.0f * b) / 9.0f;
float r = (a * (2.0f * a2 - 9.0f * b) + 27.0f * c) / 54.0f;
float r2 = r * r;
float q3 = q * q * q;
float A, B;
if (r2 < q3) {
float t = r / sqrtf(q3);
t = glm::clamp(t, -1.0f, 1.0f);
t = acosf(t);
a /= 3.0f;
q = -2.0f * sqrtf(q);
x[0] = q * cosf(t / 3.0f) - a;
x[1] = q * cosf((t + 2.0f * (float)M_PI) / 3.0f) - a;
x[2] = q * cosf((t - 2.0f * (float)M_PI) / 3.0f) - a;
return 3;
} else {
A = -powf(fabsf(r) + sqrtf(r2 - q3), 1.0f / 3.0f);
if (r < 0) {
A = -A;
}
B = (A == 0.0f ? 0.0f : q / A);
a /= 3.0f;
x[0] = (A + B) - a;
x[1] = -0.5f * (A + B) - a;
x[2] = 0.5f * sqrtf(3.0f) * (A - B);
if (fabsf(x[2]) < EPSILON) {
x[2] = x[1];
return 2;
}
return 1;
}
}
bool solve_quartic(float a, float b, float c, float d, glm::vec4& roots) {
float a3 = -b;
float b3 = a * c - 4.0f *d;
float c3 = -a * a * d - c * c + 4.0f * b * d;
float px3[3];
unsigned int iZeroes = solveP3(px3, a3, b3, c3);
float q1, q2, p1, p2, D, sqD, y;
y = px3[0];
if (iZeroes != 1) {
if (fabsf(px3[1]) > fabsf(y)) {
y = px3[1];
}
if (fabsf(px3[2]) > fabsf(y)) {
y = px3[2];
}
}
D = y * y - 4.0f * d;
if (fabsf(D) < EPSILON) {
q1 = q2 = 0.5f * y;
D = a * a - 4.0f * (b - y);
if (fabsf(D) < EPSILON) {
p1 = p2 = 0.5f * a;
} else {
sqD = sqrtf(D);
p1 = 0.5f * (a + sqD);
p2 = 0.5f * (a - sqD);
}
} else {
sqD = sqrtf(D);
q1 = 0.5f * (y + sqD);
q2 = 0.5f * (y - sqD);
p1 = (a * q1 - c) / (q1 - q2);
p2 = (c - a * q2) / (q1 - q2);
}
std::complex<float> x1, x2, x3, x4;
D = p1 * p1 - 4.0f * q1;
if (D < 0.0f) {
x1.real(-0.5f * p1);
x1.imag(0.5f * sqrtf(-D));
x2 = std::conj(x1);
} else {
sqD = sqrtf(D);
x1.real(0.5f * (-p1 + sqD));
x2.real(0.5f * (-p1 - sqD));
}
D = p2 * p2 - 4.0f * q2;
if (D < 0.0f) {
x3.real(-0.5f * p2);
x3.imag(0.5f * sqrtf(-D));
x4 = std::conj(x3);
} else {
sqD = sqrtf(D);
x3.real(0.5f * (-p2 + sqD));
x4.real(0.5f * (-p2 - sqD));
}
bool hasRealRoot = false;
if (fabsf(x1.imag()) < EPSILON) {
roots.x = x1.real();
hasRealRoot = true;
}
if (fabsf(x2.imag()) < EPSILON) {
roots.y = x2.real();
hasRealRoot = true;
}
if (fabsf(x3.imag()) < EPSILON) {
roots.z = x3.real();
hasRealRoot = true;
}
if (fabsf(x4.imag()) < EPSILON) {
roots.w = x4.real();
hasRealRoot = true;
}
return hasRealRoot;
}
bool computeRealQuarticRoots(float a, float b, float c, float d, float e, glm::vec4& roots) {
return solve_quartic(b / a, c / a, d / a, e / a, roots);
}
Reference in a new issue View git blame Copy permalink