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572 lines
25 KiB
C++
572 lines
25 KiB
C++
//
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// GeometryUtil.cpp
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// libraries/shared/src
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//
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// Created by Andrzej Kapolka on 5/21/13.
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// Copyright 2013 High Fidelity, Inc.
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//
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// Distributed under the Apache License, Version 2.0.
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// See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html
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//
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#include "GeometryUtil.h"
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#include <assert.h>
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#include <cstring>
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#include <cmath>
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#include <glm/gtx/quaternion.hpp>
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#include "NumericalConstants.h"
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glm::vec3 computeVectorFromPointToSegment(const glm::vec3& point, const glm::vec3& start, const glm::vec3& end) {
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// compute the projection of the point vector onto the segment vector
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glm::vec3 segmentVector = end - start;
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float lengthSquared = glm::dot(segmentVector, segmentVector);
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if (lengthSquared < EPSILON) {
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return start - point; // start and end the same
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}
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float proj = glm::dot(point - start, segmentVector) / lengthSquared;
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if (proj <= 0.0f) { // closest to the start
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return start - point;
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} else if (proj >= 1.0f) { // closest to the end
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return end - point;
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} else { // closest to the middle
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return start + segmentVector*proj - point;
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}
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}
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// Computes the penetration between a point and a sphere (centered at the origin)
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// if point is inside sphere: returns true and stores the result in 'penetration'
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// (the vector that would move the point outside the sphere)
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// otherwise returns false
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bool findSpherePenetration(const glm::vec3& point, const glm::vec3& defaultDirection, float sphereRadius,
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glm::vec3& penetration) {
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float vectorLength = glm::length(point);
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if (vectorLength < EPSILON) {
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penetration = defaultDirection * sphereRadius;
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return true;
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}
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float distance = vectorLength - sphereRadius;
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if (distance < 0.0f) {
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penetration = point * (-distance / vectorLength);
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return true;
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}
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return false;
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}
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bool findSpherePointPenetration(const glm::vec3& sphereCenter, float sphereRadius,
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const glm::vec3& point, glm::vec3& penetration) {
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return findSpherePenetration(point - sphereCenter, glm::vec3(0.0f, -1.0f, 0.0f), sphereRadius, penetration);
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}
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bool findPointSpherePenetration(const glm::vec3& point, const glm::vec3& sphereCenter,
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float sphereRadius, glm::vec3& penetration) {
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return findSpherePenetration(sphereCenter - point, glm::vec3(0.0f, -1.0f, 0.0f), sphereRadius, penetration);
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}
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bool findSphereSpherePenetration(const glm::vec3& firstCenter, float firstRadius,
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const glm::vec3& secondCenter, float secondRadius, glm::vec3& penetration) {
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return findSpherePointPenetration(firstCenter, firstRadius + secondRadius, secondCenter, penetration);
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}
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bool findSphereSegmentPenetration(const glm::vec3& sphereCenter, float sphereRadius,
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const glm::vec3& segmentStart, const glm::vec3& segmentEnd, glm::vec3& penetration) {
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return findSpherePenetration(computeVectorFromPointToSegment(sphereCenter, segmentStart, segmentEnd),
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glm::vec3(0.0f, -1.0f, 0.0f), sphereRadius, penetration);
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}
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bool findSphereCapsulePenetration(const glm::vec3& sphereCenter, float sphereRadius, const glm::vec3& capsuleStart,
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const glm::vec3& capsuleEnd, float capsuleRadius, glm::vec3& penetration) {
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return findSphereSegmentPenetration(sphereCenter, sphereRadius + capsuleRadius,
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capsuleStart, capsuleEnd, penetration);
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}
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bool findPointCapsuleConePenetration(const glm::vec3& point, const glm::vec3& capsuleStart,
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const glm::vec3& capsuleEnd, float startRadius, float endRadius, glm::vec3& penetration) {
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// compute the projection of the point vector onto the segment vector
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glm::vec3 segmentVector = capsuleEnd - capsuleStart;
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float lengthSquared = glm::dot(segmentVector, segmentVector);
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if (lengthSquared < EPSILON) { // start and end the same
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return findPointSpherePenetration(point, capsuleStart,
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glm::max(startRadius, endRadius), penetration);
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}
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float proj = glm::dot(point - capsuleStart, segmentVector) / lengthSquared;
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if (proj <= 0.0f) { // closest to the start
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return findPointSpherePenetration(point, capsuleStart, startRadius, penetration);
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} else if (proj >= 1.0f) { // closest to the end
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return findPointSpherePenetration(point, capsuleEnd, endRadius, penetration);
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} else { // closest to the middle
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return findPointSpherePenetration(point, capsuleStart + segmentVector * proj,
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glm::mix(startRadius, endRadius, proj), penetration);
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}
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}
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bool findSphereCapsuleConePenetration(const glm::vec3& sphereCenter,
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float sphereRadius, const glm::vec3& capsuleStart, const glm::vec3& capsuleEnd,
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float startRadius, float endRadius, glm::vec3& penetration) {
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return findPointCapsuleConePenetration(sphereCenter, capsuleStart, capsuleEnd,
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startRadius + sphereRadius, endRadius + sphereRadius, penetration);
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}
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bool findSpherePlanePenetration(const glm::vec3& sphereCenter, float sphereRadius,
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const glm::vec4& plane, glm::vec3& penetration) {
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float distance = glm::dot(plane, glm::vec4(sphereCenter, 1.0f)) - sphereRadius;
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if (distance < 0.0f) {
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penetration = glm::vec3(plane) * distance;
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return true;
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}
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return false;
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}
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bool findSphereDiskPenetration(const glm::vec3& sphereCenter, float sphereRadius,
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const glm::vec3& diskCenter, float diskRadius, float diskThickness, const glm::vec3& diskNormal,
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glm::vec3& penetration) {
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glm::vec3 localCenter = sphereCenter - diskCenter;
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float axialDistance = glm::dot(localCenter, diskNormal);
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if (std::fabs(axialDistance) < (sphereRadius + 0.5f * diskThickness)) {
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// sphere hit the plane, but does it hit the disk?
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// Note: this algorithm ignores edge hits.
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glm::vec3 axialOffset = axialDistance * diskNormal;
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if (glm::length(localCenter - axialOffset) < diskRadius) {
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// yes, hit the disk
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penetration = (std::fabs(axialDistance) - (sphereRadius + 0.5f * diskThickness) ) * diskNormal;
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if (axialDistance < 0.0f) {
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// hit the backside of the disk, so negate penetration vector
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penetration *= -1.0f;
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}
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return true;
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}
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}
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return false;
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}
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bool findCapsuleSpherePenetration(const glm::vec3& capsuleStart, const glm::vec3& capsuleEnd, float capsuleRadius,
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const glm::vec3& sphereCenter, float sphereRadius, glm::vec3& penetration) {
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if (findSphereCapsulePenetration(sphereCenter, sphereRadius,
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capsuleStart, capsuleEnd, capsuleRadius, penetration)) {
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penetration = -penetration;
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return true;
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}
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return false;
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}
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bool findCapsulePlanePenetration(const glm::vec3& capsuleStart, const glm::vec3& capsuleEnd, float capsuleRadius,
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const glm::vec4& plane, glm::vec3& penetration) {
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float distance = glm::min(glm::dot(plane, glm::vec4(capsuleStart, 1.0f)),
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glm::dot(plane, glm::vec4(capsuleEnd, 1.0f))) - capsuleRadius;
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if (distance < 0.0f) {
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penetration = glm::vec3(plane) * distance;
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return true;
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}
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return false;
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}
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glm::vec3 addPenetrations(const glm::vec3& currentPenetration, const glm::vec3& newPenetration) {
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// find the component of the new penetration in the direction of the current
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float currentLength = glm::length(currentPenetration);
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if (currentLength == 0.0f) {
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return newPenetration;
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}
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glm::vec3 currentDirection = currentPenetration / currentLength;
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float directionalComponent = glm::dot(newPenetration, currentDirection);
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// if orthogonal or in the opposite direction, we can simply add
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if (directionalComponent <= 0.0f) {
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return currentPenetration + newPenetration;
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}
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// otherwise, we need to take the maximum component of current and new
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return currentDirection * glm::max(directionalComponent, currentLength) +
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newPenetration - (currentDirection * directionalComponent);
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}
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bool findRaySphereIntersection(const glm::vec3& origin, const glm::vec3& direction,
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const glm::vec3& center, float radius, float& distance) {
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glm::vec3 relativeOrigin = origin - center;
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float c = glm::dot(relativeOrigin, relativeOrigin) - radius * radius;
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if (c < 0.0f) {
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distance = 0.0f;
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return true; // starts inside the sphere
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}
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float b = glm::dot(direction, relativeOrigin);
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float radicand = b * b - c;
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if (radicand < 0.0f) {
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return false; // doesn't hit the sphere
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}
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float t = -b - sqrtf(radicand);
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if (t < 0.0f) {
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return false; // doesn't hit the sphere
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}
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distance = t;
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return true;
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}
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bool findRayCapsuleIntersection(const glm::vec3& origin, const glm::vec3& direction,
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const glm::vec3& start, const glm::vec3& end, float radius, float& distance) {
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if (start == end) {
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return findRaySphereIntersection(origin, direction, start, radius, distance); // handle degenerate case
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}
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glm::vec3 relativeOrigin = origin - start;
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glm::vec3 relativeEnd = end - start;
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float capsuleLength = glm::length(relativeEnd);
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relativeEnd /= capsuleLength;
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float originProjection = glm::dot(relativeEnd, relativeOrigin);
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glm::vec3 constant = relativeOrigin - relativeEnd * originProjection;
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float c = glm::dot(constant, constant) - radius * radius;
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if (c < 0.0f) { // starts inside cylinder
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if (originProjection < 0.0f) { // below start
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return findRaySphereIntersection(origin, direction, start, radius, distance);
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} else if (originProjection > capsuleLength) { // above end
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return findRaySphereIntersection(origin, direction, end, radius, distance);
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} else { // between start and end
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distance = 0.0f;
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return true;
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}
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}
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glm::vec3 coefficient = direction - relativeEnd * glm::dot(relativeEnd, direction);
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float a = glm::dot(coefficient, coefficient);
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if (a == 0.0f) {
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return false; // parallel to enclosing cylinder
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}
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float b = 2.0f * glm::dot(constant, coefficient);
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float radicand = b * b - 4.0f * a * c;
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if (radicand < 0.0f) {
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return false; // doesn't hit the enclosing cylinder
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}
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float t = (-b - sqrtf(radicand)) / (2.0f * a);
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if (t < 0.0f) {
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return false; // doesn't hit the enclosing cylinder
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}
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glm::vec3 intersection = relativeOrigin + direction * t;
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float intersectionProjection = glm::dot(relativeEnd, intersection);
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if (intersectionProjection < 0.0f) { // below start
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return findRaySphereIntersection(origin, direction, start, radius, distance);
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} else if (intersectionProjection > capsuleLength) { // above end
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return findRaySphereIntersection(origin, direction, end, radius, distance);
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}
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distance = t; // between start and end
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return true;
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}
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// reference https://www.opengl.org/wiki/Calculating_a_Surface_Normal
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glm::vec3 Triangle::getNormal() const {
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glm::vec3 u = v1 - v0;
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glm::vec3 v = v2 - v0;
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glm::vec3 result;
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result.x = (u.y * v.z) - (u.z * v.y);
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result.x = (u.z * v.x) - (u.x * v.z);
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result.x = (u.x * v.y) - (u.y * v.x);
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return glm::normalize(result);
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}
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bool findRayTriangleIntersection(const glm::vec3& origin, const glm::vec3& direction,
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const glm::vec3& v0, const glm::vec3& v1, const glm::vec3& v2, float& distance) {
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glm::vec3 firstSide = v0 - v1;
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glm::vec3 secondSide = v2 - v1;
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glm::vec3 normal = glm::cross(secondSide, firstSide);
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float dividend = glm::dot(normal, v1) - glm::dot(origin, normal);
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if (dividend > 0.0f) {
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return false; // origin below plane
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}
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float divisor = glm::dot(normal, direction);
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if (divisor >= 0.0f) {
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return false;
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}
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float t = dividend / divisor;
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glm::vec3 point = origin + direction * t;
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if (glm::dot(normal, glm::cross(point - v1, firstSide)) > 0.0f &&
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glm::dot(normal, glm::cross(secondSide, point - v1)) > 0.0f &&
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glm::dot(normal, glm::cross(point - v0, v2 - v0)) > 0.0f) {
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distance = t;
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return true;
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}
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return false;
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}
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// Do line segments (r1p1.x, r1p1.y)--(r1p2.x, r1p2.y) and (r2p1.x, r2p1.y)--(r2p2.x, r2p2.y) intersect?
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// from: http://ptspts.blogspot.com/2010/06/how-to-determine-if-two-line-segments.html
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bool doLineSegmentsIntersect(glm::vec2 r1p1, glm::vec2 r1p2, glm::vec2 r2p1, glm::vec2 r2p2) {
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int d1 = computeDirection(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p1.x, r1p1.y);
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int d2 = computeDirection(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p2.x, r1p2.y);
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int d3 = computeDirection(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p1.x, r2p1.y);
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int d4 = computeDirection(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p2.x, r2p2.y);
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return (((d1 > 0 && d2 < 0) || (d1 < 0 && d2 > 0)) &&
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((d3 > 0 && d4 < 0) || (d3 < 0 && d4 > 0))) ||
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(d1 == 0 && isOnSegment(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p1.x, r1p1.y)) ||
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(d2 == 0 && isOnSegment(r2p1.x, r2p1.y, r2p2.x, r2p2.y, r1p2.x, r1p2.y)) ||
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(d3 == 0 && isOnSegment(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p1.x, r2p1.y)) ||
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(d4 == 0 && isOnSegment(r1p1.x, r1p1.y, r1p2.x, r1p2.y, r2p2.x, r2p2.y));
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}
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bool isOnSegment(float xi, float yi, float xj, float yj, float xk, float yk) {
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return (xi <= xk || xj <= xk) && (xk <= xi || xk <= xj) &&
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(yi <= yk || yj <= yk) && (yk <= yi || yk <= yj);
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}
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int computeDirection(float xi, float yi, float xj, float yj, float xk, float yk) {
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float a = (xk - xi) * (yj - yi);
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float b = (xj - xi) * (yk - yi);
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return a < b ? -1 : a > b ? 1 : 0;
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}
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//
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// Polygon Clipping routines inspired by, pseudo code found here: http://www.cs.rit.edu/~icss571/clipTrans/PolyClipBack.html
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//
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// Coverage Map's polygon coordinates are from -1 to 1 in the following mapping to screen space.
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//
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// (0,0) (windowWidth, 0)
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// -1,1 1,1
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// +-----------------------+
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// | | |
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// | | |
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// | -1,0 | |
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// |-----------+-----------|
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// | 0,0 |
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// | | |
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// | | |
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// | | |
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// +-----------------------+
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// -1,-1 1,-1
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// (0,windowHeight) (windowWidth,windowHeight)
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//
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const float PolygonClip::TOP_OF_CLIPPING_WINDOW = 1.0f;
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const float PolygonClip::BOTTOM_OF_CLIPPING_WINDOW = -1.0f;
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const float PolygonClip::LEFT_OF_CLIPPING_WINDOW = -1.0f;
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const float PolygonClip::RIGHT_OF_CLIPPING_WINDOW = 1.0f;
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const glm::vec2 PolygonClip::TOP_LEFT_CLIPPING_WINDOW ( LEFT_OF_CLIPPING_WINDOW , TOP_OF_CLIPPING_WINDOW );
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const glm::vec2 PolygonClip::TOP_RIGHT_CLIPPING_WINDOW ( RIGHT_OF_CLIPPING_WINDOW, TOP_OF_CLIPPING_WINDOW );
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const glm::vec2 PolygonClip::BOTTOM_LEFT_CLIPPING_WINDOW ( LEFT_OF_CLIPPING_WINDOW , BOTTOM_OF_CLIPPING_WINDOW );
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const glm::vec2 PolygonClip::BOTTOM_RIGHT_CLIPPING_WINDOW ( RIGHT_OF_CLIPPING_WINDOW, BOTTOM_OF_CLIPPING_WINDOW );
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void PolygonClip::clipToScreen(const glm::vec2* inputVertexArray, int inLength, glm::vec2*& outputVertexArray, int& outLength) {
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int tempLengthA = inLength;
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int tempLengthB;
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int maxLength = inLength * 2;
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glm::vec2* tempVertexArrayA = new glm::vec2[maxLength];
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glm::vec2* tempVertexArrayB = new glm::vec2[maxLength];
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// set up our temporary arrays
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memcpy(tempVertexArrayA, inputVertexArray, sizeof(glm::vec2) * inLength);
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// Left edge
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LineSegment2 edge;
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edge[0] = TOP_LEFT_CLIPPING_WINDOW;
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edge[1] = BOTTOM_LEFT_CLIPPING_WINDOW;
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// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
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sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
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// clean the array from tempVertexArrayA and copy cleaned result to tempVertexArrayA
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copyCleanArray(tempLengthA, tempVertexArrayA, tempLengthB, tempVertexArrayB);
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// Bottom Edge
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edge[0] = BOTTOM_LEFT_CLIPPING_WINDOW;
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edge[1] = BOTTOM_RIGHT_CLIPPING_WINDOW;
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// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
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sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
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// clean the array from tempVertexArrayA and copy cleaned result to tempVertexArrayA
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copyCleanArray(tempLengthA, tempVertexArrayA, tempLengthB, tempVertexArrayB);
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// Right Edge
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edge[0] = BOTTOM_RIGHT_CLIPPING_WINDOW;
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edge[1] = TOP_RIGHT_CLIPPING_WINDOW;
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// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
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sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
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// clean the array from tempVertexArrayA and copy cleaned result to tempVertexArrayA
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copyCleanArray(tempLengthA, tempVertexArrayA, tempLengthB, tempVertexArrayB);
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// Top Edge
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edge[0] = TOP_RIGHT_CLIPPING_WINDOW;
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edge[1] = TOP_LEFT_CLIPPING_WINDOW;
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// clip the array from tempVertexArrayA and copy end result to tempVertexArrayB
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sutherlandHodgmanPolygonClip(tempVertexArrayA, tempVertexArrayB, tempLengthA, tempLengthB, edge);
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// 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;
|
|
}
|
|
|
|
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);
|
|
}
|