overte/libraries/shared/src/GeometryUtil.cpp

572 lines
25 KiB
C++

//
// 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 <glm/gtx/quaternion.hpp>
#include "NumericalConstants.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);
}
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 = glm::dot(direction, relativeOrigin);
float radicand = b * b - c;
if (radicand < 0.0f) {
return false; // doesn't hit the sphere
}
float t = -b - sqrtf(radicand);
if (t < 0.0f) {
return false; // doesn't hit the sphere
}
distance = t;
return true;
}
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 u = v1 - v0;
glm::vec3 v = v2 - v0;
glm::vec3 result;
result.x = (u.y * v.z) - (u.z * v.y);
result.x = (u.z * v.x) - (u.x * v.z);
result.x = (u.x * v.y) - (u.y * v.x);
return glm::normalize(result);
}
bool findRayTriangleIntersection(const glm::vec3& origin, const glm::vec3& direction,
const glm::vec3& v0, const glm::vec3& v1, const glm::vec3& v2, float& distance) {
glm::vec3 firstSide = v0 - v1;
glm::vec3 secondSide = v2 - v1;
glm::vec3 normal = glm::cross(secondSide, firstSide);
float dividend = glm::dot(normal, v1) - glm::dot(origin, normal);
if (dividend > 0.0f) {
return false; // origin below plane
}
float divisor = glm::dot(normal, direction);
if (divisor >= 0.0f) {
return false;
}
float t = dividend / divisor;
glm::vec3 point = origin + direction * t;
if (glm::dot(normal, glm::cross(point - v1, firstSide)) > 0.0f &&
glm::dot(normal, glm::cross(secondSide, point - v1)) > 0.0f &&
glm::dot(normal, glm::cross(point - v0, v2 - v0)) > 0.0f) {
distance = t;
return true;
}
return false;
}
// 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 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
memcpy(tempVertexArrayA, inputVertexArray, sizeof(glm::vec2) * inLength);
// 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;
}
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);
}