/* -*- 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
