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gecko/gfx/2d/Matrix.cpp

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/* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 2 -*-
* 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
using namespace std;
namespace {
/* 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);
}
} // namespace
namespace mozilla {
namespace gfx {
std::ostream&
operator<<(std::ostream& aStream, const Matrix& aMatrix)
{
return aStream << "[ " << aMatrix._11
<< " " << aMatrix._12
<< "; " << aMatrix._21
<< " " << aMatrix._22
<< "; " << aMatrix._31
<< " " << aMatrix._32
<< "; ]";
}
std::ostream&
operator<<(std::ostream& aStream, const Matrix4x4& aMatrix)
{
const Float *f = &aMatrix._11;
aStream << "[ " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ]" << std::endl;
return aStream;
}
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;
}
Rect
Matrix::TransformBounds(const Rect &aRect) const
{
int i;
Point quad[4];
Float min_x, max_x;
Float min_y, max_y;
quad[0] = *this * aRect.TopLeft();
quad[1] = *this * aRect.TopRight();
quad[2] = *this * aRect.BottomLeft();
quad[3] = *this * aRect.BottomRight();
min_x = max_x = quad[0].x;
min_y = max_y = quad[0].y;
for (i = 1; i < 4; i++) {
if (quad[i].x < min_x)
min_x = quad[i].x;
if (quad[i].x > max_x)
max_x = quad[i].x;
if (quad[i].y < min_y)
min_y = quad[i].y;
if (quad[i].y > max_y)
max_y = quad[i].y;
}
return Rect(min_x, min_y, max_x - min_x, max_y - min_y);
}
Matrix&
Matrix::NudgeToIntegers()
{
NudgeToInteger(&_11);
NudgeToInteger(&_12);
NudgeToInteger(&_21);
NudgeToInteger(&_22);
NudgeToInteger(&_31);
NudgeToInteger(&_32);
return *this;
}
template<class F>
RectTyped<UnknownUnits, F>
Matrix4x4::TransformBounds(const RectTyped<UnknownUnits, F>& aRect) const
{
Point4DTyped<UnknownUnits, F> verts[4];
verts[0] = *this * Point4DTyped<UnknownUnits, F>(aRect.x, aRect.y, 0.0, 1.0);
verts[1] = *this * Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.y, 0.0, 1.0);
verts[2] = *this * Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.YMost(), 0.0, 1.0);
verts[3] = *this * Point4DTyped<UnknownUnits, F>(aRect.x, aRect.YMost(), 0.0, 1.0);
PointTyped<UnknownUnits, F> quad[4];
F min_x, max_x;
F min_y, max_y;
quad[0] = *this * aRect.TopLeft();
quad[1] = *this * aRect.TopRight();
quad[2] = *this * aRect.BottomLeft();
quad[3] = *this * aRect.BottomRight();
min_x = max_x = quad[0].x;
min_y = max_y = quad[0].y;
for (int i = 1; i < 4; i++) {
if (quad[i].x < min_x) {
min_x = quad[i].x;
}
if (quad[i].x > max_x) {
max_x = quad[i].x;
}
if (quad[i].y < min_y) {
min_y = quad[i].y;
}
if (quad[i].y > max_y) {
max_y = quad[i].y;
}
}
return RectTyped<UnknownUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y);
}
template<class F>
Point4DTyped<UnknownUnits, F>
ComputePerspectivePlaneIntercept(const Point4DTyped<UnknownUnits, F>& aFirst,
const Point4DTyped<UnknownUnits, F>& aSecond)
{
// This function will always return a point with a w value of 0.
// The X, Y, and Z components will point towards an infinite vanishing
// point.
// We want to interpolate aFirst and aSecond to find the point intersecting
// with the w=0 plane.
// Since we know what we want the w component to be, we can rearrange the
// interpolation equation and solve for t.
float t = -aFirst.w / (aSecond.w - aFirst.w);
// Use t to find the remainder of the components
return aFirst + (aSecond - aFirst) * t;
}
template <class F>
RectTyped<UnknownUnits, F>
Matrix4x4::ProjectRectBounds(const RectTyped<UnknownUnits, F>& aRect, const RectTyped<UnknownUnits, F>& aClip) const
{
// This function must never return std::numeric_limits<Float>::max() or any
// other arbitrary large value in place of inifinity. This often occurs when
// aRect is an inversed projection matrix or when aRect is transformed to be
// partly behind and in front of the camera (w=0 plane in homogenous
// coordinates) - See Bug 1035611
// Some call-sites will call RoundGfxRectToAppRect which clips both the
// extents and dimensions of the rect to be bounded by nscoord_MAX.
// If we return a Rect that, when converted to nscoords, has a width or height
// greater than nscoord_MAX, RoundGfxRectToAppRect will clip the overflow
// off both the min and max end of the rect after clipping the extents of the
// rect, resulting in a translation of the rect towards the infinite end.
// The bounds returned by ProjectRectBounds are expected to be clipped only on
// the edges beyond the bounds of the coordinate system; otherwise, the
// clipped bounding box would be smaller than the correct one and result
// bugs such as incorrect culling (eg. Bug 1073056)
// To address this without requiring all code to work in homogenous
// coordinates or interpret infinite values correctly, a specialized
// clipping function is integrated into ProjectRectBounds.
// Callers should pass an aClip value that represents the extents to clip
// the result to, in the same coordinate system as aRect.
Point4DTyped<UnknownUnits, F> points[4];
points[0] = ProjectPoint(aRect.TopLeft());
points[1] = ProjectPoint(aRect.TopRight());
points[2] = ProjectPoint(aRect.BottomRight());
points[3] = ProjectPoint(aRect.BottomLeft());
F min_x = std::numeric_limits<F>::max();
F min_y = std::numeric_limits<F>::max();
F max_x = -std::numeric_limits<F>::max();
F max_y = -std::numeric_limits<F>::max();
for (int i=0; i<4; i++) {
// Only use points that exist above the w=0 plane
if (points[i].HasPositiveWCoord()) {
PointTyped<UnknownUnits, F> point2d = aClip.ClampPoint(points[i].As2DPoint());
min_x = std::min<F>(point2d.x, min_x);
max_x = std::max<F>(point2d.x, max_x);
min_y = std::min<F>(point2d.y, min_y);
max_y = std::max<F>(point2d.y, max_y);
}
int next = (i == 3) ? 0 : i + 1;
if (points[i].HasPositiveWCoord() != points[next].HasPositiveWCoord()) {
// If the line between two points crosses the w=0 plane, then interpolate
// to find the point of intersection with the w=0 plane and use that
// instead.
Point4DTyped<UnknownUnits, F> intercept =
ComputePerspectivePlaneIntercept(points[i], points[next]);
// Since intercept.w will always be 0 here, we interpret x,y,z as a
// direction towards an infinite vanishing point.
if (intercept.x < 0.0f) {
min_x = aClip.x;
} else if (intercept.x > 0.0f) {
max_x = aClip.XMost();
}
if (intercept.y < 0.0f) {
min_y = aClip.y;
} else if (intercept.y > 0.0f) {
max_y = aClip.YMost();
}
}
}
if (max_x < min_x || max_y < min_y) {
return RectTyped<UnknownUnits, F>(0, 0, 0, 0);
}
return RectTyped<UnknownUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y);
}
template<class F>
size_t
Matrix4x4::TransformAndClipRect(const RectTyped<UnknownUnits, F>& aRect,
const RectTyped<UnknownUnits, F>& aClip,
PointTyped<UnknownUnits, F>* aVerts) const
{
// Initialize a double-buffered array of points in homogenous space with
// the input rectangle, aRect.
Point4DTyped<UnknownUnits, F> points[2][kTransformAndClipRectMaxVerts];
Point4DTyped<UnknownUnits, F>* dstPoint = points[0];
*dstPoint++ = *this * Point4DTyped<UnknownUnits, F>(aRect.x, aRect.y, 0, 1);
*dstPoint++ = *this * Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.y, 0, 1);
*dstPoint++ = *this * Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.YMost(), 0, 1);
*dstPoint++ = *this * Point4DTyped<UnknownUnits, F>(aRect.x, aRect.YMost(), 0, 1);
// View frustum clipping planes are described as normals originating from
// the 0,0,0,0 origin.
Point4DTyped<UnknownUnits, F> planeNormals[4];
planeNormals[0] = Point4DTyped<UnknownUnits, F>(1.0, 0.0, 0.0, -aClip.x);
planeNormals[1] = Point4DTyped<UnknownUnits, F>(-1.0, 0.0, 0.0, aClip.XMost());
planeNormals[2] = Point4DTyped<UnknownUnits, F>(0.0, 1.0, 0.0, -aClip.y);
planeNormals[3] = Point4DTyped<UnknownUnits, F>(0.0, -1.0, 0.0, aClip.YMost());
// Iterate through each clipping plane and clip the polygon.
// In each pass, we double buffer, alternating between points[0] and
// points[1].
for (int plane=0; plane < 4; plane++) {
planeNormals[plane].Normalize();
Point4DTyped<UnknownUnits, F>* srcPoint = points[plane & 1];
Point4DTyped<UnknownUnits, F>* srcPointEnd = dstPoint;
dstPoint = points[~plane & 1];
Point4DTyped<UnknownUnits, F>* prevPoint = srcPointEnd - 1;
F prevDot = planeNormals[plane].DotProduct(*prevPoint);
while (srcPoint < srcPointEnd) {
F nextDot = planeNormals[plane].DotProduct(*srcPoint);
if ((nextDot >= 0.0) != (prevDot >= 0.0)) {
// An intersection with the clipping plane has been detected.
// Interpolate to find the intersecting point and emit it.
F t = -prevDot / (nextDot - prevDot);
*dstPoint++ = *srcPoint * t + *prevPoint * (1.0 - t);
}
if (nextDot >= 0.0) {
// Emit any source points that are on the positive side of the
// clipping plane.
*dstPoint++ = *srcPoint;
}
prevPoint = srcPoint++;
prevDot = nextDot;
}
}
size_t dstPointCount = 0;
size_t srcPointCount = dstPoint - points[0];
for (Point4DTyped<UnknownUnits, F>* srcPoint = points[0]; srcPoint < points[0] + srcPointCount; srcPoint++) {
PointTyped<UnknownUnits, F> p;
if (srcPoint->w == 0.0) {
// If a point lies on the intersection of the clipping planes at
// (0,0,0,0), we must avoid a division by zero w component.
p = PointTyped<UnknownUnits, F>(0.0, 0.0);
} else {
p = srcPoint->As2DPoint();
}
// Emit only unique points
if (dstPointCount == 0 || p != aVerts[dstPointCount - 1]) {
aVerts[dstPointCount++] = p;
}
}
return dstPointCount;
}
bool
Matrix4x4::Invert()
{
Float det = Determinant();
if (!det) {
return false;
}
Matrix4x4 result;
result._11 = _23 * _34 * _42 - _24 * _33 * _42 + _24 * _32 * _43 - _22 * _34 * _43 - _23 * _32 * _44 + _22 * _33 * _44;
result._12 = _14 * _33 * _42 - _13 * _34 * _42 - _14 * _32 * _43 + _12 * _34 * _43 + _13 * _32 * _44 - _12 * _33 * _44;
result._13 = _13 * _24 * _42 - _14 * _23 * _42 + _14 * _22 * _43 - _12 * _24 * _43 - _13 * _22 * _44 + _12 * _23 * _44;
result._14 = _14 * _23 * _32 - _13 * _24 * _32 - _14 * _22 * _33 + _12 * _24 * _33 + _13 * _22 * _34 - _12 * _23 * _34;
result._21 = _24 * _33 * _41 - _23 * _34 * _41 - _24 * _31 * _43 + _21 * _34 * _43 + _23 * _31 * _44 - _21 * _33 * _44;
result._22 = _13 * _34 * _41 - _14 * _33 * _41 + _14 * _31 * _43 - _11 * _34 * _43 - _13 * _31 * _44 + _11 * _33 * _44;
result._23 = _14 * _23 * _41 - _13 * _24 * _41 - _14 * _21 * _43 + _11 * _24 * _43 + _13 * _21 * _44 - _11 * _23 * _44;
result._24 = _13 * _24 * _31 - _14 * _23 * _31 + _14 * _21 * _33 - _11 * _24 * _33 - _13 * _21 * _34 + _11 * _23 * _34;
result._31 = _22 * _34 * _41 - _24 * _32 * _41 + _24 * _31 * _42 - _21 * _34 * _42 - _22 * _31 * _44 + _21 * _32 * _44;
result._32 = _14 * _32 * _41 - _12 * _34 * _41 - _14 * _31 * _42 + _11 * _34 * _42 + _12 * _31 * _44 - _11 * _32 * _44;
result._33 = _12 * _24 * _41 - _14 * _22 * _41 + _14 * _21 * _42 - _11 * _24 * _42 - _12 * _21 * _44 + _11 * _22 * _44;
result._34 = _14 * _22 * _31 - _12 * _24 * _31 - _14 * _21 * _32 + _11 * _24 * _32 + _12 * _21 * _34 - _11 * _22 * _34;
result._41 = _23 * _32 * _41 - _22 * _33 * _41 - _23 * _31 * _42 + _21 * _33 * _42 + _22 * _31 * _43 - _21 * _32 * _43;
result._42 = _12 * _33 * _41 - _13 * _32 * _41 + _13 * _31 * _42 - _11 * _33 * _42 - _12 * _31 * _43 + _11 * _32 * _43;
result._43 = _13 * _22 * _41 - _12 * _23 * _41 - _13 * _21 * _42 + _11 * _23 * _42 + _12 * _21 * _43 - _11 * _22 * _43;
result._44 = _12 * _23 * _31 - _13 * _22 * _31 + _13 * _21 * _32 - _11 * _23 * _32 - _12 * _21 * _33 + _11 * _22 * _33;
result._11 /= det;
result._12 /= det;
result._13 /= det;
result._14 /= det;
result._21 /= det;
result._22 /= det;
result._23 /= det;
result._24 /= det;
result._31 /= det;
result._32 /= det;
result._33 /= det;
result._34 /= det;
result._41 /= det;
result._42 /= det;
result._43 /= det;
result._44 /= det;
*this = result;
return true;
}
void
Matrix4x4::SetNAN()
{
_11 = UnspecifiedNaN<Float>();
_21 = UnspecifiedNaN<Float>();
_31 = UnspecifiedNaN<Float>();
_41 = UnspecifiedNaN<Float>();
_12 = UnspecifiedNaN<Float>();
_22 = UnspecifiedNaN<Float>();
_32 = UnspecifiedNaN<Float>();
_42 = UnspecifiedNaN<Float>();
_13 = UnspecifiedNaN<Float>();
_23 = UnspecifiedNaN<Float>();
_33 = UnspecifiedNaN<Float>();
_43 = UnspecifiedNaN<Float>();
_14 = UnspecifiedNaN<Float>();
_24 = UnspecifiedNaN<Float>();
_34 = UnspecifiedNaN<Float>();
_44 = UnspecifiedNaN<Float>();
}
void
Matrix4x4::SetRotationFromQuaternion(const Quaternion& q)
{
const Float x2 = q.x + q.x, y2 = q.y + q.y, z2 = q.z + q.z;
const Float xx = q.x * x2, xy = q.x * y2, xz = q.x * z2;
const Float yy = q.y * y2, yz = q.y * z2, zz = q.z * z2;
const Float wx = q.w * x2, wy = q.w * y2, wz = q.w * z2;
_11 = 1.0f - (yy + zz);
_21 = xy + wz;
_31 = xz - wy;
_41 = 0.0f;
_12 = xy - wz;
_22 = 1.0f - (xx + zz);
_32 = yz + wx;
_42 = 0.0f;
_13 = xz + wy;
_23 = yz - wx;
_33 = 1.0f - (xx + yy);
_43 = 0.0f;
_14 = _42 = _43 = 0.0f;
_44 = 1.0f;
}
void
Matrix4x4::SkewXY(double aXSkew, double aYSkew)
{
// XXX Is double precision really necessary here
float tanX = SafeTangent(aXSkew);
float tanY = SafeTangent(aYSkew);
float temp;
temp = _11;
_11 += tanY * _21;
_21 += tanX * temp;
temp = _12;
_12 += tanY * _22;
_22 += tanX * temp;
temp = _13;
_13 += tanY * _23;
_23 += tanX * temp;
temp = _14;
_14 += tanY * _24;
_24 += tanX * temp;
}
void
Matrix4x4::RotateX(double aTheta)
{
// XXX Is double precision really necessary here
double cosTheta = FlushToZero(cos(aTheta));
double sinTheta = FlushToZero(sin(aTheta));
float temp;
temp = _21;
_21 = cosTheta * _21 + sinTheta * _31;
_31 = -sinTheta * temp + cosTheta * _31;
temp = _22;
_22 = cosTheta * _22 + sinTheta * _32;
_32 = -sinTheta * temp + cosTheta * _32;
temp = _23;
_23 = cosTheta * _23 + sinTheta * _33;
_33 = -sinTheta * temp + cosTheta * _33;
temp = _24;
_24 = cosTheta * _24 + sinTheta * _34;
_34 = -sinTheta * temp + cosTheta * _34;
}
void
Matrix4x4::RotateY(double aTheta)
{
// XXX Is double precision really necessary here
double cosTheta = FlushToZero(cos(aTheta));
double sinTheta = FlushToZero(sin(aTheta));
float temp;
temp = _11;
_11 = cosTheta * _11 + -sinTheta * _31;
_31 = sinTheta * temp + cosTheta * _31;
temp = _12;
_12 = cosTheta * _12 + -sinTheta * _32;
_32 = sinTheta * temp + cosTheta * _32;
temp = _13;
_13 = cosTheta * _13 + -sinTheta * _33;
_33 = sinTheta * temp + cosTheta * _33;
temp = _14;
_14 = cosTheta * _14 + -sinTheta * _34;
_34 = sinTheta * temp + cosTheta * _34;
}
void
Matrix4x4::RotateZ(double aTheta)
{
// XXX Is double precision really necessary here
double cosTheta = FlushToZero(cos(aTheta));
double sinTheta = FlushToZero(sin(aTheta));
float temp;
temp = _11;
_11 = cosTheta * _11 + sinTheta * _21;
_21 = -sinTheta * temp + cosTheta * _21;
temp = _12;
_12 = cosTheta * _12 + sinTheta * _22;
_22 = -sinTheta * temp + cosTheta * _22;
temp = _13;
_13 = cosTheta * _13 + sinTheta * _23;
_23 = -sinTheta * temp + cosTheta * _23;
temp = _14;
_14 = cosTheta * _14 + sinTheta * _24;
_24 = -sinTheta * temp + cosTheta * _24;
}
void
Matrix4x4::Perspective(float aDepth)
{
MOZ_ASSERT(aDepth > 0.0f, "Perspective must be positive!");
_31 += -1.0/aDepth * _41;
_32 += -1.0/aDepth * _42;
_33 += -1.0/aDepth * _43;
_34 += -1.0/aDepth * _44;
}
Point3D
Matrix4x4::GetNormalVector() const
{
// Define a plane in transformed space as the transformations
// of 3 points on the z=0 screen plane.
Point3D a = *this * Point3D(0, 0, 0);
Point3D b = *this * Point3D(0, 1, 0);
Point3D c = *this * Point3D(1, 0, 0);
// Convert to two vectors on the surface of the plane.
Point3D ab = b - a;
Point3D ac = c - a;
return ac.CrossProduct(ab);
}
template<class F>
RectTyped<UnknownUnits, F>
Matrix4x4::TransformAndClipBounds(const RectTyped<UnknownUnits, F>& aRect,
const RectTyped<UnknownUnits, F>& aClip) const
{
PointTyped<UnknownUnits, F> verts[kTransformAndClipRectMaxVerts];
size_t vertCount = TransformAndClipRect(aRect, aClip, verts);
F min_x = std::numeric_limits<F>::max();
F min_y = std::numeric_limits<F>::max();
F max_x = -std::numeric_limits<F>::max();
F max_y = -std::numeric_limits<F>::max();
for (size_t i=0; i < vertCount; i++) {
min_x = std::min(min_x, verts[i].x);
max_x = std::max(max_x, verts[i].x);
min_y = std::min(min_y, verts[i].y);
max_y = std::max(max_y, verts[i].y);
}
if (max_x < min_x || max_y < min_y) {
return RectTyped<UnknownUnits, F>(0, 0, 0, 0);
}
return RectTyped<UnknownUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y);
}
// Explicit template instantiation for float and double precision
template
size_t
Matrix4x4::TransformAndClipRect(const Rect& aRect, const Rect& aClip,
Point* aVerts) const;
template
size_t
Matrix4x4::TransformAndClipRect(const RectDouble& aRect,
const RectDouble& aClip,
PointDouble* aVerts) const;
template
Rect
Matrix4x4::TransformAndClipBounds(const Rect& aRect,
const Rect& aClip) const;
template
RectDouble
Matrix4x4::TransformAndClipBounds(const RectDouble& aRect,
const RectDouble& aClip) const;
template
Rect
Matrix4x4::TransformBounds(const Rect& aRect) const;
template
RectDouble
Matrix4x4::TransformBounds(const RectDouble& aRect) const;
template
Rect
Matrix4x4::ProjectRectBounds(const Rect& aRect, const Rect& aClip) const;
template
RectDouble
Matrix4x4::ProjectRectBounds(const RectDouble& aRect, const RectDouble& aClip) const;
} // namespace gfx
} // namespace mozilla
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