142 lines
7.0 KiB
C++
Executable File
142 lines
7.0 KiB
C++
Executable File
/********************************************************************************
|
|
* ReactPhysics3D physics library, http://www.reactphysics3d.com *
|
|
* Copyright (c) 2010-2020 Daniel Chappuis *
|
|
*********************************************************************************
|
|
* *
|
|
* This software is provided 'as-is', without any express or implied warranty. *
|
|
* In no event will the authors be held liable for any damages arising from the *
|
|
* use of this software. *
|
|
* *
|
|
* Permission is granted to anyone to use this software for any purpose, *
|
|
* including commercial applications, and to alter it and redistribute it *
|
|
* freely, subject to the following restrictions: *
|
|
* *
|
|
* 1. The origin of this software must not be misrepresented; you must not claim *
|
|
* that you wrote the original software. If you use this software in a *
|
|
* product, an acknowledgment in the product documentation would be *
|
|
* appreciated but is not required. *
|
|
* *
|
|
* 2. Altered source versions must be plainly marked as such, and must not be *
|
|
* misrepresented as being the original software. *
|
|
* *
|
|
* 3. This notice may not be removed or altered from any source distribution. *
|
|
* *
|
|
********************************************************************************/
|
|
|
|
#ifndef REACTPHYSICS3D_MATHEMATICS_FUNCTIONS_H
|
|
#define REACTPHYSICS3D_MATHEMATICS_FUNCTIONS_H
|
|
|
|
// Libraries
|
|
#include <reactphysics3d/configuration.h>
|
|
#include <reactphysics3d/decimal.h>
|
|
#include <algorithm>
|
|
#include <cassert>
|
|
#include <cmath>
|
|
#include <reactphysics3d/containers/List.h>
|
|
|
|
/// ReactPhysics3D namespace
|
|
namespace reactphysics3d {
|
|
|
|
struct Vector3;
|
|
struct Vector2;
|
|
|
|
// ---------- Mathematics functions ---------- //
|
|
|
|
/// Function to test if two real numbers are (almost) equal
|
|
/// We test if two numbers a and b are such that (a-b) are in [-EPSILON; EPSILON]
|
|
inline bool approxEqual(decimal a, decimal b, decimal epsilon = MACHINE_EPSILON) {
|
|
return (std::fabs(a - b) < epsilon);
|
|
}
|
|
|
|
/// Function to test if two vectors are (almost) equal
|
|
bool approxEqual(const Vector3& vec1, const Vector3& vec2, decimal epsilon = MACHINE_EPSILON);
|
|
|
|
/// Function to test if two vectors are (almost) equal
|
|
bool approxEqual(const Vector2& vec1, const Vector2& vec2, decimal epsilon = MACHINE_EPSILON);
|
|
|
|
/// Function that returns the result of the "value" clamped by
|
|
/// two others values "lowerLimit" and "upperLimit"
|
|
inline int clamp(int value, int lowerLimit, int upperLimit) {
|
|
assert(lowerLimit <= upperLimit);
|
|
return std::min(std::max(value, lowerLimit), upperLimit);
|
|
}
|
|
|
|
/// Function that returns the result of the "value" clamped by
|
|
/// two others values "lowerLimit" and "upperLimit"
|
|
inline decimal clamp(decimal value, decimal lowerLimit, decimal upperLimit) {
|
|
assert(lowerLimit <= upperLimit);
|
|
return std::min(std::max(value, lowerLimit), upperLimit);
|
|
}
|
|
|
|
/// Return the minimum value among three values
|
|
inline decimal min3(decimal a, decimal b, decimal c) {
|
|
return std::min(std::min(a, b), c);
|
|
}
|
|
|
|
/// Return the maximum value among three values
|
|
inline decimal max3(decimal a, decimal b, decimal c) {
|
|
return std::max(std::max(a, b), c);
|
|
}
|
|
|
|
/// Return true if two values have the same sign
|
|
inline bool sameSign(decimal a, decimal b) {
|
|
return a * b >= decimal(0.0);
|
|
}
|
|
|
|
/// Return true if two vectors are parallel
|
|
bool areParallelVectors(const Vector3& vector1, const Vector3& vector2);
|
|
|
|
/// Return true if two vectors are orthogonal
|
|
bool areOrthogonalVectors(const Vector3& vector1, const Vector3& vector2);
|
|
|
|
/// Clamp a vector such that it is no longer than a given maximum length
|
|
Vector3 clamp(const Vector3& vector, decimal maxLength);
|
|
|
|
// Compute and return a point on segment from "segPointA" and "segPointB" that is closest to point "pointC"
|
|
Vector3 computeClosestPointOnSegment(const Vector3& segPointA, const Vector3& segPointB, const Vector3& pointC);
|
|
|
|
// Compute the closest points between two segments
|
|
void computeClosestPointBetweenTwoSegments(const Vector3& seg1PointA, const Vector3& seg1PointB,
|
|
const Vector3& seg2PointA, const Vector3& seg2PointB,
|
|
Vector3& closestPointSeg1, Vector3& closestPointSeg2);
|
|
|
|
/// Compute the barycentric coordinates u, v, w of a point p inside the triangle (a, b, c)
|
|
void computeBarycentricCoordinatesInTriangle(const Vector3& a, const Vector3& b, const Vector3& c,
|
|
const Vector3& p, decimal& u, decimal& v, decimal& w);
|
|
|
|
/// Compute the intersection between a plane and a segment
|
|
decimal computePlaneSegmentIntersection(const Vector3& segA, const Vector3& segB, const decimal planeD, const Vector3& planeNormal);
|
|
|
|
/// Compute the distance between a point and a line
|
|
decimal computePointToLineDistance(const Vector3& linePointA, const Vector3& linePointB, const Vector3& point);
|
|
|
|
/// Clip a segment against multiple planes and return the clipped segment vertices
|
|
List<Vector3> clipSegmentWithPlanes(const Vector3& segA, const Vector3& segB,
|
|
const List<Vector3>& planesPoints,
|
|
const List<Vector3>& planesNormals,
|
|
MemoryAllocator& allocator);
|
|
|
|
/// Clip a polygon against multiple planes and return the clipped polygon vertices
|
|
List<Vector3> clipPolygonWithPlanes(const List<Vector3>& polygonVertices, const List<Vector3>& planesPoints,
|
|
const List<Vector3>& planesNormals, MemoryAllocator& allocator);
|
|
|
|
/// Project a point onto a plane that is given by a point and its unit length normal
|
|
Vector3 projectPointOntoPlane(const Vector3& point, const Vector3& planeNormal, const Vector3& planePoint);
|
|
|
|
/// Return the distance between a point and a plane (the plane normal must be normalized)
|
|
decimal computePointToPlaneDistance(const Vector3& point, const Vector3& planeNormal, const Vector3& planePoint);
|
|
|
|
/// Return true if the given number is prime
|
|
bool isPrimeNumber(int number);
|
|
|
|
/// Return an unique integer from two integer numbers (pairing function)
|
|
/// Here we assume that the two parameter numbers are sorted such that
|
|
/// number1 = max(number1, number2)
|
|
/// http://szudzik.com/ElegantPairing.pdf
|
|
uint64 pairNumbers(uint32 number1, uint32 number2);
|
|
|
|
}
|
|
|
|
|
|
#endif
|