203 lines
7.8 KiB
C++
203 lines
7.8 KiB
C++
/********************************************************************************
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* ReactPhysics3D physics library, http://www.reactphysics3d.com *
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* Copyright (c) 2010-2016 Daniel Chappuis *
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*********************************************************************************
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* *
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* This software is provided 'as-is', without any express or implied warranty. *
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* In no event will the authors be held liable for any damages arising from the *
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* use of this software. *
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* *
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* Permission is granted to anyone to use this software for any purpose, *
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* including commercial applications, and to alter it and redistribute it *
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* freely, subject to the following restrictions: *
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* *
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* 1. The origin of this software must not be misrepresented; you must not claim *
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* that you wrote the original software. If you use this software in a *
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* product, an acknowledgment in the product documentation would be *
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* appreciated but is not required. *
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* *
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* 2. Altered source versions must be plainly marked as such, and must not be *
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* misrepresented as being the original software. *
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* *
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* 3. This notice may not be removed or altered from any source distribution. *
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* *
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********************************************************************************/
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// Libraries
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#include "mathematics_functions.h"
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#include "Vector3.h"
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#include <cassert>
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using namespace reactphysics3d;
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/// Compute the barycentric coordinates u, v, w of a point p inside the triangle (a, b, c)
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/// This method uses the technique described in the book Real-Time collision detection by
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/// Christer Ericson.
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void reactphysics3d::computeBarycentricCoordinatesInTriangle(const Vector3& a, const Vector3& b, const Vector3& c,
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const Vector3& p, decimal& u, decimal& v, decimal& w) {
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const Vector3 v0 = b - a;
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const Vector3 v1 = c - a;
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const Vector3 v2 = p - a;
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decimal d00 = v0.dot(v0);
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decimal d01 = v0.dot(v1);
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decimal d11 = v1.dot(v1);
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decimal d20 = v2.dot(v0);
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decimal d21 = v2.dot(v1);
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decimal denom = d00 * d11 - d01 * d01;
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v = (d11 * d20 - d01 * d21) / denom;
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w = (d00 * d21 - d01 * d20) / denom;
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u = decimal(1.0) - v - w;
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}
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/// Clamp a vector such that it is no longer than a given maximum length
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Vector3 reactphysics3d::clamp(const Vector3& vector, decimal maxLength) {
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if (vector.lengthSquare() > maxLength * maxLength) {
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return vector.getUnit() * maxLength;
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}
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return vector;
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}
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/// Compute and return a point on segment from "segPointA" and "segPointB" that is closest to point "pointC"
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Vector3 reactphysics3d::computeClosestPointOnSegment(const Vector3& segPointA, const Vector3& segPointB, const Vector3& pointC) {
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const Vector3 ab = segPointB - segPointA;
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decimal abLengthSquare = ab.lengthSquare();
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// If the segment has almost zero length
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if (abLengthSquare < MACHINE_EPSILON) {
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// Return one end-point of the segment as the closest point
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return segPointA;
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}
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// Project point C onto "AB" line
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decimal t = (pointC - segPointA).dot(ab) / abLengthSquare;
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// If projected point onto the line is outside the segment, clamp it to the segment
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if (t < decimal(0.0)) t = decimal(0.0);
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if (t > decimal(1.0)) t = decimal(1.0);
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// Return the closest point on the segment
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return segPointA + t * ab;
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}
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/// Compute the closest points between two segments
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/// This method uses the technique described in the book Real-Time
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/// collision detection by Christer Ericson.
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void reactphysics3d::computeClosestPointBetweenTwoSegments(const Vector3& seg1PointA, const Vector3& seg1PointB,
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const Vector3& seg2PointA, const Vector3& seg2PointB,
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Vector3& closestPointSeg1, Vector3& closestPointSeg2) {
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const Vector3 d1 = seg1PointB - seg1PointA;
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const Vector3 d2 = seg2PointB - seg2PointA;
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const Vector3 r = seg1PointA - seg2PointA;
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decimal a = d1.lengthSquare();
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decimal e = d2.lengthSquare();
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decimal f = d2.dot(r);
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decimal s, t;
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// If both segments degenerate into points
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if (a <= MACHINE_EPSILON && e <= MACHINE_EPSILON) {
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closestPointSeg1 = seg1PointA;
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closestPointSeg2 = seg2PointA;
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return;
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}
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if (a <= MACHINE_EPSILON) { // If first segment degenerates into a point
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s = decimal(0.0);
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// Compute the closest point on second segment
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t = clamp(f / e, decimal(0.0), decimal(1.0));
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}
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else {
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decimal c = d1.dot(r);
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// If the second segment degenerates into a point
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if (e <= MACHINE_EPSILON) {
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t = decimal(0.0);
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s = clamp(-c / a, decimal(0.0), decimal(1.0));
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}
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else {
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decimal b = d1.dot(d2);
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decimal denom = a * e - b * b;
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// If the segments are not parallel
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if (denom != decimal(0.0)) {
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// Compute the closest point on line 1 to line 2 and
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// clamp to first segment.
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s = clamp((b * f - c * e) / denom, decimal(0.0), decimal(1.0));
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}
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else {
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// Pick an arbitrary point on first segment
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s = decimal(0.0);
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}
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// Compute the point on line 2 closest to the closest point
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// we have just found
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t = (b * s + f) / e;
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// If this closest point is inside second segment (t in [0, 1]), we are done.
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// Otherwise, we clamp the point to the second segment and compute again the
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// closest point on segment 1
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if (t < decimal(0.0)) {
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t = decimal(0.0);
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s = clamp(-c / a, decimal(0.0), decimal(1.0));
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}
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else if (t > decimal(1.0)) {
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t = decimal(1.0);
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s = clamp((b - c) / a, decimal(0.0), decimal(1.0));
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}
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}
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}
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// Compute the closest points on both segments
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closestPointSeg1 = seg1PointA + d1 * s;
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closestPointSeg2 = seg2PointA + d2 * t;
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}
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/// Compute the intersection between a plane and a segment
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// Let the plane define by the equation planeNormal.dot(X) = planeD with X a point on the plane and "planeNormal" the plane normal. This method
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// computes the intersection P between the plane and the segment (segA, segB). The method returns the value "t" such
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// that P = segA + t * (segB - segA). Note that it only returns a value in [0, 1] if there is an intersection. Otherwise,
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// there is no intersection between the plane and the segment.
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decimal reactphysics3d::computePlaneSegmentIntersection(const Vector3& segA, const Vector3& segB, const decimal planeD, const Vector3& planeNormal) {
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const decimal parallelEpsilon = decimal(0.0001);
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decimal t = decimal(-1);
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// Segment AB
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const Vector3 ab = segB - segA;
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decimal nDotAB = planeNormal.dot(ab);
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// If the segment is not parallel to the plane
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if (nDotAB > parallelEpsilon) {
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t = (planeD - planeNormal.dot(segA)) / nDotAB;
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}
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return t;
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}
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/// Compute the distance between a point "point" and a line given by the points "linePointA" and "linePointB"
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decimal reactphysics3d::computeDistancePointToLineDistance(const Vector3& linePointA, const Vector3& linePointB, const Vector3& point) {
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decimal distAB = (linePointB - linePointA).length();
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if (distAB < MACHINE_EPSILON) {
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return (point - linePointA).length();
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}
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return ((point - linePointA).cross(point - linePointB)).length() / distAB;
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}
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