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git-svn-id: https://reactphysics3d.googlecode.com/svn/trunk@250 92aac97c-a6ce-11dd-a772-7fcde58d38e6

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chappuis.daniel 2010-01-26 15:17:57 +00:00
parent 4e5d485016
commit 5fe08fef0a
1 changed files with 116 additions and 2 deletions
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118
sources/reactphysics3d/mathematics/mathematics.h
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@ -77,6 +77,64 @@ inline void closestPointsBetweenTwoLines(const reactphysics3d::Vector3D& point1,
*beta = (a*f-b*c)/d;
}
// TODO : Test this method
// This method returns true if the point "P" is on the segment between "segPointA" and "segPointB" and return false otherwise
inline bool isPointOnSegment(const reactphysics3d::Vector3D& segPointA, const reactphysics3d::Vector3D& segPointB, const reactphysics3d::Vector3D& P) {
// Check if the point P is on the line between "segPointA" and "segPointB"
reactphysics3d::Vector3D d = segPointB - segPointA;
reactphysics3d::Vector3D dP = P - segPointA;
if (!d.isParallelWith(dP)) {
return false;
}
// Compute the length of the segment
double segmentLength = d.length();
// Compute the distance from point "P" to points "segPointA" and "segPointB"
double distA = dP.length();
double distB = (P - segPointB).length();
// If one of the "distA" and "distB" is greather than the length of the segment, then P is not on the segment
if (distA > segmentLength || distB > segmentLength) {
return false;
}
// Otherwise, the point P is on the segment
return true;
}
// TODO : Test this method
// Given two segments in 3D that are not parallel and that intersect, this method computes the intersection point between the two segments
// The result intersection point is the reference "resultPoint".
inline void computeNonParallelSegmentsIntersection(const reactphysics3d::Vector3D& seg1PointA, const reactphysics3d::Vector3D& seg1PointB,
const reactphysics3d::Vector3D& seg2PointA, const reactphysics3d::Vector3D& seg2PointB,
reactphysics3d::Vector3D& resultPoint) {
// Determine the lines of both segments
reactphysics3d::Vector3D d1 = seg1PointB - seg1PointA;
reactphysics3d::Vector3D d2 = seg2PointB - seg2PointA;
// The segments must not be parallel
assert(!d1.isParallelWith(d2));
// Compute the closet points between the two lines
double alpha, beta;
closestPointsBetweenTwoLines(seg1PointA, d1, seg2PointA, d2, &alpha, &beta);
reactphysics3d::Vector3D point1 = seg1PointA + alpha * d1;
reactphysics3d::Vector3D point2 = seg2PointA + beta * d2;
// The closest points have to be on the segments, otherwise there is no intersection between the segments
assert(isPointOnSegment(seg1PointA, seg1PointB, point1));
assert(isPointOnSegment(seg2PointA, seg2PointB, point2));
// If the two closest point aren't very close, there is no intersection between the segments
reactphysics3d::Vector3D d = point2 - point1;
assert(d.length() <= EPSILON);
// They are very close so we return the intersection point (halfway between "point1" and "point2"
resultPoint = 0.5 * (point1 + point2);
}
/*
// TODO : Test this method
// Move a set of points by a given vector.
@ -114,8 +172,8 @@ inline reactphysics3d::Vector3D computeOrthogonalProjectionOfPointOntoALine(cons
// and "resultPointB". Because the two given segments don't have to be on the same exact line, the result intersection segment will a segment
// halway between the first and the second given segments.
inline void computeParallelSegmentsIntersection(const reactphysics3d::Vector3D& seg1PointA, const reactphysics3d::Vector3D& seg1PointB,
const reactphysics3d::Vector3D& seg2PointA, const reactphysics3d::Vector3D& seg2PointB,
reactphysics3d::Vector3D& resultPointA, reactphysics3d::Vector3D& resultPointB) {
const reactphysics3d::Vector3D& seg2PointA, const reactphysics3d::Vector3D& seg2PointB,
reactphysics3d::Vector3D& resultPointA, reactphysics3d::Vector3D& resultPointB) {
// Compute the segment vectors
reactphysics3d::Vector3D d1 = seg1PointB - seg1PointA;
reactphysics3d::Vector3D d2 = seg2PointB - seg2PointA;
@ -157,5 +215,61 @@ inline void computeParallelSegmentsIntersection(const reactphysics3d::Vector3D&
resultPointB = seg2PointB - 0.5 * v;
}
}
// TODO : Test this method
// This method uses the Sutherland-Hodgman clipping algorithm to clip a subject polygon (given by the ordered 3D vertices in "subjectPolygon") using
// a rectangle polygon (given by the ordered 3D vertices in "clipRectangle"). The subject polygon and the clip rectangle are in 3D but we assumed that
// they are on a same plane in 3D. The method returns the ordered 3D vertices of the subject polygon clipped using the rectangle polygon.
inline std::vector<reactphysics3d::Vector3D> clipPolygonWithRectangleInPlane(const std::vector<reactphysics3d::Vector3D>& subjectPolygon, const std::vector<reactphysics3d::Vector3D>& clipRectangle) {
assert(clipRectangle.size() == 4);
std::vector<reactphysics3d::Vector3D> outputPolygon;
std::vector<reactphysics3d::Vector3D> inputPolygon = subjectPolygon;
// For each edge of the clip rectangle
for (unsigned int i=0; i<4; ++i) {
// Each edge defines a clip plane. The clip plane is define by a point on this plane (a vertice of the current edge) and
// a plane normal (because we are using a clip rectangle, the plane normal is the next edge of the clip rectangle).
reactphysics3d::Vector3D planeNormal = clipRectangle[(i+2) % 4] - clipRectangle[(i+1) % 4];
reactphysics3d::Vector3D A = clipRectangle[i]; // Segment AB is the current segment of the "clipRectangle"
reactphysics3d::Vector3D B = clipRectangle[(i+1) % 4];
reactphysics3d::Vector3D S = inputPolygon[i];
// For each vertex of the subject polygon
for (unsigned int j=0; j<subjectPolygon.size(); ++j) {
reactphysics3d::Vector3D P = inputPolygon[(i+1) % inputPolygon.size()];
// If the point P is inside the clip plane
if (planeNormal.scalarProduct(P-A) > 0.0) {
// If the point S is also inside the clip plane
if (planeNormal.scalarProduct(S-A) > 0.0) {
outputPolygon.push_back(P);
}
else { // If the point S is outside the clip plane
// Compute the intersection point between the segment SP and the clip plane
reactphysics3d::Vector3D intersectPoint;
computeNonParallelSegmentsIntersection(S, P, A, B, intersectPoint);
outputPolygon.push_back(intersectPoint);
outputPolygon.push_back(P);
}
}
else if (planeNormal.scalarProduct(S-A) > 0.0) {
// Compute the intersection point between the segment SP and the clip plane
reactphysics3d::Vector3D intersectPoint;
computeNonParallelSegmentsIntersection(S, P, A, B, intersectPoint);
outputPolygon.push_back(intersectPoint);
}
S = P;
}
inputPolygon = outputPolygon;
}
// Return the clipped polygon
return outputPolygon;
}
#endif