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/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
#include "Matrix.h"
#include "Quaternion.h"
#include "Tools.h"
#include <algorithm>
#include <ostream>
#include <math.h>
#include <float.h> // for FLT_EPSILON
#include "mozilla/FloatingPoint.h" // for UnspecifiedNaN
namespace mozilla {
namespace gfx {
/* Force small values to zero. We do this to avoid having sin(360deg)
* evaluate to a tiny but nonzero value.
*/
double FlushToZero(double aVal) {
// XXX Is double precision really necessary here
if (-FLT_EPSILON < aVal && aVal < FLT_EPSILON) {
return 0.0f;
} else {
return aVal;
}
}
/* Computes tan(aTheta). For values of aTheta such that tan(aTheta) is
* undefined or very large, SafeTangent returns a manageably large value
* of the correct sign.
*/
double SafeTangent(double aTheta) {
// XXX Is double precision really necessary here
const double kEpsilon = 0.0001;
/* tan(theta) = sin(theta)/cos(theta); problems arise when
* cos(theta) is too close to zero. Limit cos(theta) to the
* range [-1, -epsilon] U [epsilon, 1].
*/
double sinTheta = sin(aTheta);
double cosTheta = cos(aTheta);
if (cosTheta >= 0 && cosTheta < kEpsilon) {
cosTheta = kEpsilon;
} else if (cosTheta < 0 && cosTheta >= -kEpsilon) {
cosTheta = -kEpsilon;
}
return FlushToZero(sinTheta / cosTheta);
}
template <>
Matrix Matrix::Rotation(Float aAngle) {
Matrix newMatrix;
Float s = sinf(aAngle);
Float c = cosf(aAngle);
newMatrix._11 = c;
newMatrix._12 = s;
newMatrix._21 = -s;
newMatrix._22 = c;
return newMatrix;
}
template <>
MatrixDouble MatrixDouble::Rotation(Double aAngle) {
MatrixDouble newMatrix;
Double s = sin(aAngle);
Double c = cos(aAngle);
newMatrix._11 = c;
newMatrix._12 = s;
newMatrix._21 = -s;
newMatrix._22 = c;
return newMatrix;
}
template <>
Matrix4x4 MatrixDouble::operator*(const Matrix4x4& aMatrix) const {
Matrix4x4 resultMatrix;
resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21;
resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22;
resultMatrix._13 = this->_11 * aMatrix._13 + this->_12 * aMatrix._23;
resultMatrix._14 = this->_11 * aMatrix._14 + this->_12 * aMatrix._24;
resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21;
resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22;
resultMatrix._23 = this->_21 * aMatrix._13 + this->_22 * aMatrix._23;
resultMatrix._24 = this->_21 * aMatrix._14 + this->_22 * aMatrix._24;
resultMatrix._31 = aMatrix._31;
resultMatrix._32 = aMatrix._32;
resultMatrix._33 = aMatrix._33;
resultMatrix._34 = aMatrix._34;
resultMatrix._41 =
this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + aMatrix._41;
resultMatrix._42 =
this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + aMatrix._42;
resultMatrix._43 =
this->_31 * aMatrix._13 + this->_32 * aMatrix._23 + aMatrix._43;
resultMatrix._44 =
this->_31 * aMatrix._14 + this->_32 * aMatrix._24 + aMatrix._44;
return resultMatrix;
}
// Intersect the polygon given by aPoints with the half space induced by
// aPlaneNormal and return the resulting polygon. The returned points are
// stored in aDestBuffer, and its meaningful subspan is returned.
template <typename F>
Span<Point4DTyped<UnknownUnits, F>> IntersectPolygon(
Span<Point4DTyped<UnknownUnits, F>> aPoints,
const Point4DTyped<UnknownUnits, F>& aPlaneNormal,
Span<Point4DTyped<UnknownUnits, F>> aDestBuffer) {
if (aPoints.Length() < 1 || aDestBuffer.Length() < 1) {
return {};
}
size_t nextIndex = 0; // aDestBuffer[nextIndex] is the next emitted point.
// Iterate over the polygon edges. In each iteration the current edge
// is the edge from *prevPoint to point. If the two end points lie on
// different sides of the plane, we have an intersection. Otherwise,
// the edge is either completely "inside" the half-space created by
// the clipping plane, and we add curPoint, or it is completely
// "outside", and we discard curPoint. This loop can create duplicated
// points in the polygon.
const auto* prevPoint = &aPoints[aPoints.Length() - 1];
F prevDot = aPlaneNormal.DotProduct(*prevPoint);
for (const auto& curPoint : aPoints) {
F curDot = aPlaneNormal.DotProduct(curPoint);
if ((curDot >= 0.0) != (prevDot >= 0.0)) {
// An intersection with the clipping plane has been detected.
// Interpolate to find the intersecting curPoint and emit it.
F t = -prevDot / (curDot - prevDot);
aDestBuffer[nextIndex++] = curPoint * t + *prevPoint * (1.0 - t);
if (nextIndex >= aDestBuffer.Length()) {
break;
}
}
if (curDot >= 0.0) {
// Emit any source points that are on the positive side of the
// clipping plane.
aDestBuffer[nextIndex++] = curPoint;
if (nextIndex >= aDestBuffer.Length()) {
break;
}
}
prevPoint = &curPoint;
prevDot = curDot;
}
return aDestBuffer.To(nextIndex);
}
template Span<Point4DTyped<UnknownUnits, Float>> IntersectPolygon(
Span<Point4DTyped<UnknownUnits, Float>> aPoints,
const Point4DTyped<UnknownUnits, Float>& aPlaneNormal,
Span<Point4DTyped<UnknownUnits, Float>> aDestBuffer);
template Span<Point4DTyped<UnknownUnits, Double>> IntersectPolygon(
Span<Point4DTyped<UnknownUnits, Double>> aPoints,
const Point4DTyped<UnknownUnits, Double>& aPlaneNormal,
Span<Point4DTyped<UnknownUnits, Double>> aDestBuffer);
} // namespace gfx
} // namespace mozilla