size_t linearProgram2(const std::vector<Line>& lines, float radius, const Vector2& optVelocity, bool directionOpt, Vector2& result)
{
if (directionOpt) {
/*
* Optimize direction. Note that the optimization velocity is of unit
* length in this case.
*/
result = optVelocity * radius;
} else if (absSq(optVelocity) > sqr(radius)) {
/* Optimize closest point and outside circle. */
result = normalize(optVelocity) * radius;
} else {
/* Optimize closest point and inside circle. */
result = optVelocity;
}
for (size_t i = 0; i < lines.size(); ++i) {
if (det(lines[i].direction, lines[i].point - result) > 0.0f) {
/* Result does not satisfy constraint i. Compute new optimal result. */
const Vector2 tempResult = result;
if (!linearProgram1(lines, i, radius, optVelocity, directionOpt, result)) {
result = tempResult;
return i;
}
}
}
return lines.size();
}
bool linearProgram2(const std::vector<Plane> &planes, size_t planeNo, float radius, const Vector3 &optVelocity, bool directionOpt, Vector3 &result)
{
const float planeDist = planes[planeNo].point * planes[planeNo].normal;
const float planeDistSq = sqr(planeDist);
const float radiusSq = sqr(radius);
if (planeDistSq > radiusSq) {
/* Max speed sphere fully invalidates plane planeNo. */
return false;
}
const float planeRadiusSq = radiusSq - planeDistSq;
const Vector3 planeCenter = planeDist * planes[planeNo].normal;
if (directionOpt) {
/* Project direction optVelocity on plane planeNo. */
const Vector3 planeOptVelocity = optVelocity - (optVelocity * planes[planeNo].normal) * planes[planeNo].normal;
const float planeOptVelocityLengthSq = absSq(planeOptVelocity);
if (planeOptVelocityLengthSq <= RVO_EPSILON) {
result = planeCenter;
}
else {
result = planeCenter + std::sqrt(planeRadiusSq / planeOptVelocityLengthSq) * planeOptVelocity;
}
}
else {
/* Project point optVelocity on plane planeNo. */
result = optVelocity + ((planes[planeNo].point - optVelocity) * planes[planeNo].normal) * planes[planeNo].normal;
/* If outside planeCircle, project on planeCircle. */
if (absSq(result) > radiusSq) {
const Vector3 planeResult = result - planeCenter;
const float planeResultLengthSq = absSq(planeResult);
result = planeCenter + std::sqrt(planeRadiusSq / planeResultLengthSq) * planeResult;
}
}
for (size_t i = 0; i < planeNo; ++i) {
if (planes[i].normal * (planes[i].point - result) > 0.0f) {
/* Result does not satisfy constraint i. Compute new optimal result. */
/* Compute intersection line of plane i and plane planeNo. */
Vector3 crossProduct = cross(planes[i].normal, planes[planeNo].normal);
if (absSq(crossProduct) <= RVO_EPSILON) {
/* Planes planeNo and i are (almost) parallel, and plane i fully invalidates plane planeNo. */
return false;
}
Line line;
line.direction = normalize(crossProduct);
const Vector3 lineNormal = cross(line.direction, planes[planeNo].normal);
line.point = planes[planeNo].point + (((planes[i].point - planes[planeNo].point) * planes[i].normal) / (lineNormal * planes[i].normal)) * lineNormal;
if (!linearProgram1(planes, i, line, radius, optVelocity, directionOpt, result)) {
return false;
}
}
}
return true;
}
