Quelle Matrix.cpp Sprache: C

/* -*- 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

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