src/utils/SkCamera.cpp - platform/external/skia - Gitiles

 /*
  * Copyright 2006 The Android Open Source Project
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */

 #include "SkCamera.h"

 static SkScalar SkScalarDotDiv(int count, const SkScalar a[], int step_a,
                                const SkScalar b[], int step_b,
                                SkScalar denom) {
     SkScalar prod = 0;
     for (int i = 0; i < count; i++) {
         prod += a[0] * b[0];
         a += step_a;
         b += step_b;
     }
     return prod / denom;
 }

 static SkScalar SkScalarDot(int count, const SkScalar a[], int step_a,
                                        const SkScalar b[], int step_b) {
     SkScalar prod = 0;
     for (int i = 0; i < count; i++) {
         prod += a[0] * b[0];
         a += step_a;
         b += step_b;
     }
     return prod;
 }

 ///////////////////////////////////////////////////////////////////////////////

 SkScalar SkPoint3D::normalize(SkUnit3D* unit) const {
     SkScalar mag = SkScalarSqrt(fX*fX + fY*fY + fZ*fZ);
     if (mag) {
         SkScalar scale = SkScalarInvert(mag);
         unit->fX = fX * scale;
         unit->fY = fY * scale;
         unit->fZ = fZ * scale;
     } else {
         unit->fX = unit->fY = unit->fZ = 0;
     }
     return mag;
 }

 SkScalar SkUnit3D::Dot(const SkUnit3D& a, const SkUnit3D& b) {
     return a.fX * b.fX + a.fY * b.fY + a.fZ * b.fZ;
 }

 void SkUnit3D::Cross(const SkUnit3D& a, const SkUnit3D& b, SkUnit3D* cross) {
     SkASSERT(cross);

     // use x,y,z, in case &a == cross or &b == cross

     SkScalar x = a.fY * b.fZ - a.fZ * b.fY;
     SkScalar y = a.fZ * b.fX - a.fX * b.fY;
     SkScalar z = a.fX * b.fY - a.fY * b.fX;

     cross->set(x, y, z);
 }

 ///////////////////////////////////////////////////////////////////////////////

 SkPatch3D::SkPatch3D() {
     this->reset();
 }

 void SkPatch3D::reset() {
     fOrigin.set(0, 0, 0);
     fU.set(SK_Scalar1, 0, 0);
     fV.set(0, -SK_Scalar1, 0);
 }

 void SkPatch3D::transform(const SkMatrix3D& m, SkPatch3D* dst) const {
     if (dst == nullptr) {
         dst = (SkPatch3D*)this;
     }
     m.mapVector(fU, &dst->fU);
     m.mapVector(fV, &dst->fV);
     m.mapPoint(fOrigin, &dst->fOrigin);
 }

 SkScalar SkPatch3D::dotWith(SkScalar dx, SkScalar dy, SkScalar dz) const {
     SkScalar cx = fU.fY * fV.fZ - fU.fZ * fV.fY;
     SkScalar cy = fU.fZ * fV.fX - fU.fX * fV.fY;
     SkScalar cz = fU.fX * fV.fY - fU.fY * fV.fX;

     return cx * dx + cy * dy + cz * dz;
 }

 ///////////////////////////////////////////////////////////////////////////////

 void SkMatrix3D::reset() {
     memset(fMat, 0, sizeof(fMat));
     fMat[0][0] = fMat[1][1] = fMat[2][2] = SK_Scalar1;
 }

 void SkMatrix3D::setTranslate(SkScalar x, SkScalar y, SkScalar z) {
     memset(fMat, 0, sizeof(fMat));
     fMat[0][0] = x;
     fMat[1][1] = y;
     fMat[2][2] = z;
 }

 void SkMatrix3D::setRotateX(SkScalar degX) {
     SkScalar    s, c;

     s = SkScalarSinCos(SkDegreesToRadians(degX), &c);
     this->setRow(0, SK_Scalar1, 0, 0);
     this->setRow(1, 0, c, -s);
     this->setRow(2, 0, s, c);
 }

 void SkMatrix3D::setRotateY(SkScalar degY) {
     SkScalar    s, c;

     s = SkScalarSinCos(SkDegreesToRadians(degY), &c);
     this->setRow(0, c, 0, -s);
     this->setRow(1, 0, SK_Scalar1, 0);
     this->setRow(2, s, 0, c);
 }

 void SkMatrix3D::setRotateZ(SkScalar degZ) {
     SkScalar    s, c;

     s = SkScalarSinCos(SkDegreesToRadians(degZ), &c);
     this->setRow(0, c, -s, 0);
     this->setRow(1, s, c, 0);
     this->setRow(2, 0, 0, SK_Scalar1);
 }

 void SkMatrix3D::preTranslate(SkScalar x, SkScalar y, SkScalar z) {
     SkScalar col[3] = { x, y, z};

     for (int i = 0; i < 3; i++) {
         fMat[i][3] += SkScalarDot(3, &fMat[i][0], 1, col, 1);
     }
 }

 void SkMatrix3D::preRotateX(SkScalar degX) {
     SkMatrix3D m;
     m.setRotateX(degX);
     this->setConcat(*this, m);
 }

 void SkMatrix3D::preRotateY(SkScalar degY) {
     SkMatrix3D m;
     m.setRotateY(degY);
     this->setConcat(*this, m);
 }

 void SkMatrix3D::preRotateZ(SkScalar degZ) {
     SkMatrix3D m;
     m.setRotateZ(degZ);
     this->setConcat(*this, m);
 }

 void SkMatrix3D::setConcat(const SkMatrix3D& a, const SkMatrix3D& b) {
     SkMatrix3D  tmp;
     SkMatrix3D* c = this;

     if (this == &a || this == &b) {
         c = &tmp;
     }
     for (int i = 0; i < 3; i++) {
         for (int j = 0; j < 3; j++) {
             c->fMat[i][j] = SkScalarDot(3, &a.fMat[i][0], 1, &b.fMat[0][j], 4);
         }
         c->fMat[i][3] = SkScalarDot(3, &a.fMat[i][0], 1,
                                     &b.fMat[0][3], 4) + a.fMat[i][3];
     }

     if (c == &tmp) {
         *this = tmp;
     }
 }

 void SkMatrix3D::mapPoint(const SkPoint3D& src, SkPoint3D* dst) const {
     SkScalar x = SkScalarDot(3, &fMat[0][0], 1, &src.fX, 1) + fMat[0][3];
     SkScalar y = SkScalarDot(3, &fMat[1][0], 1, &src.fX, 1) + fMat[1][3];
     SkScalar z = SkScalarDot(3, &fMat[2][0], 1, &src.fX, 1) + fMat[2][3];
     dst->set(x, y, z);
 }

 void SkMatrix3D::mapVector(const SkVector3D& src, SkVector3D* dst) const {
     SkScalar x = SkScalarDot(3, &fMat[0][0], 1, &src.fX, 1);
     SkScalar y = SkScalarDot(3, &fMat[1][0], 1, &src.fX, 1);
     SkScalar z = SkScalarDot(3, &fMat[2][0], 1, &src.fX, 1);
     dst->set(x, y, z);
 }

 ///////////////////////////////////////////////////////////////////////////////

 SkCamera3D::SkCamera3D() {
     this->reset();
 }

 void SkCamera3D::reset() {
     fLocation.set(0, 0, -SkIntToScalar(576));   // 8 inches backward
     fAxis.set(0, 0, SK_Scalar1);                // forward
     fZenith.set(0, -SK_Scalar1, 0);             // up

     fObserver.set(0, 0, fLocation.fZ);

     fNeedToUpdate = true;
 }

 void SkCamera3D::update() {
     fNeedToUpdate = true;
 }

 void SkCamera3D::doUpdate() const {
     SkUnit3D    axis, zenith, cross;

     // construct a orthonormal basis of cross (x), zenith (y), and axis (z)
     fAxis.normalize(&axis);

     {
         SkScalar dot = SkUnit3D::Dot(SkUnit3D{fZenith.fX, fZenith.fY, fZenith.fZ}, axis);

         zenith.fX = fZenith.fX - dot * axis.fX;
         zenith.fY = fZenith.fY - dot * axis.fY;
         zenith.fZ = fZenith.fZ - dot * axis.fZ;

         SkPoint3D{zenith.fX, zenith.fY, zenith.fZ}.normalize(&zenith);
     }

     SkUnit3D::Cross(axis, zenith, &cross);

     {
         SkMatrix* orien = &fOrientation;
         SkScalar x = fObserver.fX;
         SkScalar y = fObserver.fY;
         SkScalar z = fObserver.fZ;

         // Looking along the view axis we have:
         //
         //   /|\ zenith
         //    |
         //    |
         //    |  * observer (projected on XY plane)
         //    |
         //    |____________\ cross
         //                 /
         //
         // So this does a z-shear along the view axis based on the observer's x and y values,
         // and scales in x and y relative to the negative of the observer's z value
         // (the observer is in the negative z direction).

         orien->set(SkMatrix::kMScaleX, x * axis.fX - z * cross.fX);
         orien->set(SkMatrix::kMSkewX,  x * axis.fY - z * cross.fY);
         orien->set(SkMatrix::kMTransX, x * axis.fZ - z * cross.fZ);
         orien->set(SkMatrix::kMSkewY,  y * axis.fX - z * zenith.fX);
         orien->set(SkMatrix::kMScaleY, y * axis.fY - z * zenith.fY);
         orien->set(SkMatrix::kMTransY, y * axis.fZ - z * zenith.fZ);
         orien->set(SkMatrix::kMPersp0, axis.fX);
         orien->set(SkMatrix::kMPersp1, axis.fY);
         orien->set(SkMatrix::kMPersp2, axis.fZ);
     }
 }

 void SkCamera3D::patchToMatrix(const SkPatch3D& quilt, SkMatrix* matrix) const {
     if (fNeedToUpdate) {
         this->doUpdate();
         fNeedToUpdate = false;
     }

     const SkScalar* mapPtr = (const SkScalar*)(const void*)&fOrientation;
     const SkScalar* patchPtr;
     SkPoint3D       diff;
     SkScalar        dot;

     diff.fX = quilt.fOrigin.fX - fLocation.fX;
     diff.fY = quilt.fOrigin.fY - fLocation.fY;
     diff.fZ = quilt.fOrigin.fZ - fLocation.fZ;

     dot = SkUnit3D::Dot(SkUnit3D{diff.fX,   diff.fY,   diff.fZ},
                         SkUnit3D{mapPtr[6], mapPtr[7], mapPtr[8]});

     // This multiplies fOrientation by the matrix [quilt.fU quilt.fV diff] -- U, V, and diff are
     // column vectors in the matrix -- then divides by the length of the projection of diff onto
     // the view axis (which is 'dot'). This transforms the patch (which transforms from local path
     // space to world space) into view space (since fOrientation transforms from world space to
     // view space).
     //
     // The divide by 'dot' isn't strictly necessary as the homogeneous divide would do much the
     // same thing (it's just scaling the entire matrix by 1/dot). It looks like it's normalizing
     // the matrix into some canonical space.
     patchPtr = (const SkScalar*)&quilt;
     matrix->set(SkMatrix::kMScaleX, SkScalarDotDiv(3, patchPtr, 1, mapPtr, 1, dot));
     matrix->set(SkMatrix::kMSkewY,  SkScalarDotDiv(3, patchPtr, 1, mapPtr+3, 1, dot));
     matrix->set(SkMatrix::kMPersp0, SkScalarDotDiv(3, patchPtr, 1, mapPtr+6, 1, dot));

     patchPtr += 3;
     matrix->set(SkMatrix::kMSkewX,  SkScalarDotDiv(3, patchPtr, 1, mapPtr, 1, dot));
     matrix->set(SkMatrix::kMScaleY, SkScalarDotDiv(3, patchPtr, 1, mapPtr+3, 1, dot));
     matrix->set(SkMatrix::kMPersp1, SkScalarDotDiv(3, patchPtr, 1, mapPtr+6, 1, dot));

     patchPtr = (const SkScalar*)(const void*)&diff;
     matrix->set(SkMatrix::kMTransX, SkScalarDotDiv(3, patchPtr, 1, mapPtr, 1, dot));
     matrix->set(SkMatrix::kMTransY, SkScalarDotDiv(3, patchPtr, 1, mapPtr+3, 1, dot));
     matrix->set(SkMatrix::kMPersp2, SK_Scalar1);
 }

 ///////////////////////////////////////////////////////////////////////////////

 Sk3DView::Sk3DView() {
     fInitialRec.fMatrix.reset();
     fRec = &fInitialRec;
 }

 Sk3DView::~Sk3DView() {
     Rec* rec = fRec;
     while (rec != &fInitialRec) {
         Rec* next = rec->fNext;
         delete rec;
         rec = next;
     }
 }

 void Sk3DView::save() {
     Rec* rec = new Rec;
     rec->fNext = fRec;
     rec->fMatrix = fRec->fMatrix;
     fRec = rec;
 }

 void Sk3DView::restore() {
     SkASSERT(fRec != &fInitialRec);
     Rec* next = fRec->fNext;
     delete fRec;
     fRec = next;
 }

 #ifdef SK_BUILD_FOR_ANDROID
 void Sk3DView::setCameraLocation(SkScalar x, SkScalar y, SkScalar z) {
     // the camera location is passed in inches, set in pt
     SkScalar lz = z * 72.0f;
     fCamera.fLocation.set(x * 72.0f, y * 72.0f, lz);
     fCamera.fObserver.set(0, 0, lz);
     fCamera.update();

 }

 SkScalar Sk3DView::getCameraLocationX() {
     return fCamera.fLocation.fX / 72.0f;
 }

 SkScalar Sk3DView::getCameraLocationY() {
     return fCamera.fLocation.fY / 72.0f;
 }

 SkScalar Sk3DView::getCameraLocationZ() {
     return fCamera.fLocation.fZ / 72.0f;
 }
 #endif

 void Sk3DView::translate(SkScalar x, SkScalar y, SkScalar z) {
     fRec->fMatrix.preTranslate(x, y, z);
 }

 void Sk3DView::rotateX(SkScalar deg) {
     fRec->fMatrix.preRotateX(deg);
 }

 void Sk3DView::rotateY(SkScalar deg) {
     fRec->fMatrix.preRotateY(deg);
 }

 void Sk3DView::rotateZ(SkScalar deg) {
     fRec->fMatrix.preRotateZ(deg);
 }

 SkScalar Sk3DView::dotWithNormal(SkScalar x, SkScalar y, SkScalar z) const {
     SkPatch3D   patch;
     patch.transform(fRec->fMatrix);
     return patch.dotWith(x, y, z);
 }

 void Sk3DView::getMatrix(SkMatrix* matrix) const {
     if (matrix != nullptr) {
         SkPatch3D   patch;
         patch.transform(fRec->fMatrix);
         fCamera.patchToMatrix(patch, matrix);
     }
 }

 #include "SkCanvas.h"

 void Sk3DView::applyToCanvas(SkCanvas* canvas) const {
     SkMatrix    matrix;

     this->getMatrix(&matrix);
     canvas->concat(matrix);
 }
	/*
	* Copyright 2006 The Android Open Source Project
	*
	* Use of this source code is governed by a BSD-style license that can be
	* found in the LICENSE file.
	*/

	#include "SkCamera.h"

	static SkScalar SkScalarDotDiv(int count, const SkScalar a[], int step_a,
	const SkScalar b[], int step_b,
	SkScalar denom) {
	SkScalar prod = 0;
	for (int i = 0; i < count; i++) {
	prod += a[0] * b[0];
	a += step_a;
	b += step_b;
	}
	return prod / denom;
	}

	static SkScalar SkScalarDot(int count, const SkScalar a[], int step_a,
	const SkScalar b[], int step_b) {
	SkScalar prod = 0;
	for (int i = 0; i < count; i++) {
	prod += a[0] * b[0];
	a += step_a;
	b += step_b;
	}
	return prod;
	}

	///////////////////////////////////////////////////////////////////////////////

	SkScalar SkPoint3D::normalize(SkUnit3D* unit) const {
	SkScalar mag = SkScalarSqrt(fXfX + fYfY + fZ*fZ);
	if (mag) {
	SkScalar scale = SkScalarInvert(mag);
	unit->fX = fX * scale;
	unit->fY = fY * scale;
	unit->fZ = fZ * scale;
	} else {
	unit->fX = unit->fY = unit->fZ = 0;
	}
	return mag;
	}

	SkScalar SkUnit3D::Dot(const SkUnit3D& a, const SkUnit3D& b) {
	return a.fX * b.fX + a.fY * b.fY + a.fZ * b.fZ;
	}

	void SkUnit3D::Cross(const SkUnit3D& a, const SkUnit3D& b, SkUnit3D* cross) {
	SkASSERT(cross);

	// use x,y,z, in case &a == cross or &b == cross

	SkScalar x = a.fY * b.fZ - a.fZ * b.fY;
	SkScalar y = a.fZ * b.fX - a.fX * b.fY;
	SkScalar z = a.fX * b.fY - a.fY * b.fX;

	cross->set(x, y, z);
	}

	///////////////////////////////////////////////////////////////////////////////

	SkPatch3D::SkPatch3D() {
	this->reset();
	}

	void SkPatch3D::reset() {
	fOrigin.set(0, 0, 0);
	fU.set(SK_Scalar1, 0, 0);
	fV.set(0, -SK_Scalar1, 0);
	}

	void SkPatch3D::transform(const SkMatrix3D& m, SkPatch3D* dst) const {
	if (dst == nullptr) {
	dst = (SkPatch3D*)this;
	}
	m.mapVector(fU, &dst->fU);
	m.mapVector(fV, &dst->fV);
	m.mapPoint(fOrigin, &dst->fOrigin);
	}

	SkScalar SkPatch3D::dotWith(SkScalar dx, SkScalar dy, SkScalar dz) const {
	SkScalar cx = fU.fY * fV.fZ - fU.fZ * fV.fY;
	SkScalar cy = fU.fZ * fV.fX - fU.fX * fV.fY;
	SkScalar cz = fU.fX * fV.fY - fU.fY * fV.fX;

	return cx * dx + cy * dy + cz * dz;
	}

	///////////////////////////////////////////////////////////////////////////////

	void SkMatrix3D::reset() {
	memset(fMat, 0, sizeof(fMat));
	fMat[0][0] = fMat[1][1] = fMat[2][2] = SK_Scalar1;
	}

	void SkMatrix3D::setTranslate(SkScalar x, SkScalar y, SkScalar z) {
	memset(fMat, 0, sizeof(fMat));
	fMat[0][0] = x;
	fMat[1][1] = y;
	fMat[2][2] = z;
	}

	void SkMatrix3D::setRotateX(SkScalar degX) {
	SkScalar s, c;

	s = SkScalarSinCos(SkDegreesToRadians(degX), &c);
	this->setRow(0, SK_Scalar1, 0, 0);
	this->setRow(1, 0, c, -s);
	this->setRow(2, 0, s, c);
	}

	void SkMatrix3D::setRotateY(SkScalar degY) {
	SkScalar s, c;

	s = SkScalarSinCos(SkDegreesToRadians(degY), &c);
	this->setRow(0, c, 0, -s);
	this->setRow(1, 0, SK_Scalar1, 0);
	this->setRow(2, s, 0, c);
	}

	void SkMatrix3D::setRotateZ(SkScalar degZ) {
	SkScalar s, c;

	s = SkScalarSinCos(SkDegreesToRadians(degZ), &c);
	this->setRow(0, c, -s, 0);
	this->setRow(1, s, c, 0);
	this->setRow(2, 0, 0, SK_Scalar1);
	}

	void SkMatrix3D::preTranslate(SkScalar x, SkScalar y, SkScalar z) {
	SkScalar col[3] = { x, y, z};

	for (int i = 0; i < 3; i++) {
	fMat[i][3] += SkScalarDot(3, &fMat[i][0], 1, col, 1);
	}
	}

	void SkMatrix3D::preRotateX(SkScalar degX) {
	SkMatrix3D m;
	m.setRotateX(degX);
	this->setConcat(*this, m);
	}

	void SkMatrix3D::preRotateY(SkScalar degY) {
	SkMatrix3D m;
	m.setRotateY(degY);
	this->setConcat(*this, m);
	}

	void SkMatrix3D::preRotateZ(SkScalar degZ) {
	SkMatrix3D m;
	m.setRotateZ(degZ);
	this->setConcat(*this, m);
	}

	void SkMatrix3D::setConcat(const SkMatrix3D& a, const SkMatrix3D& b) {
	SkMatrix3D tmp;
	SkMatrix3D* c = this;

	if (this == &a \|\| this == &b) {
	c = &tmp;
	}
	for (int i = 0; i < 3; i++) {
	for (int j = 0; j < 3; j++) {
	c->fMat[i][j] = SkScalarDot(3, &a.fMat[i][0], 1, &b.fMat[0][j], 4);
	}
	c->fMat[i][3] = SkScalarDot(3, &a.fMat[i][0], 1,
	&b.fMat[0][3], 4) + a.fMat[i][3];
	}

	if (c == &tmp) {
	*this = tmp;
	}
	}

	void SkMatrix3D::mapPoint(const SkPoint3D& src, SkPoint3D* dst) const {
	SkScalar x = SkScalarDot(3, &fMat[0][0], 1, &src.fX, 1) + fMat[0][3];
	SkScalar y = SkScalarDot(3, &fMat[1][0], 1, &src.fX, 1) + fMat[1][3];
	SkScalar z = SkScalarDot(3, &fMat[2][0], 1, &src.fX, 1) + fMat[2][3];
	dst->set(x, y, z);
	}

	void SkMatrix3D::mapVector(const SkVector3D& src, SkVector3D* dst) const {
	SkScalar x = SkScalarDot(3, &fMat[0][0], 1, &src.fX, 1);
	SkScalar y = SkScalarDot(3, &fMat[1][0], 1, &src.fX, 1);
	SkScalar z = SkScalarDot(3, &fMat[2][0], 1, &src.fX, 1);
	dst->set(x, y, z);
	}

	///////////////////////////////////////////////////////////////////////////////

	SkCamera3D::SkCamera3D() {
	this->reset();
	}

	void SkCamera3D::reset() {
	fLocation.set(0, 0, -SkIntToScalar(576)); // 8 inches backward
	fAxis.set(0, 0, SK_Scalar1); // forward
	fZenith.set(0, -SK_Scalar1, 0); // up

	fObserver.set(0, 0, fLocation.fZ);

	fNeedToUpdate = true;
	}

	void SkCamera3D::update() {
	fNeedToUpdate = true;
	}

	void SkCamera3D::doUpdate() const {
	SkUnit3D axis, zenith, cross;

	// construct a orthonormal basis of cross (x), zenith (y), and axis (z)
	fAxis.normalize(&axis);

	{
	SkScalar dot = SkUnit3D::Dot(SkUnit3D{fZenith.fX, fZenith.fY, fZenith.fZ}, axis);

	zenith.fX = fZenith.fX - dot * axis.fX;
	zenith.fY = fZenith.fY - dot * axis.fY;
	zenith.fZ = fZenith.fZ - dot * axis.fZ;

	SkPoint3D{zenith.fX, zenith.fY, zenith.fZ}.normalize(&zenith);
	}

	SkUnit3D::Cross(axis, zenith, &cross);

	{
	SkMatrix* orien = &fOrientation;
	SkScalar x = fObserver.fX;
	SkScalar y = fObserver.fY;
	SkScalar z = fObserver.fZ;

	// Looking along the view axis we have:
	//
	// /\|\ zenith
	// \|
	// \|
	// \| * observer (projected on XY plane)
	// \|
	// \|____________\ cross
	// /
	//
	// So this does a z-shear along the view axis based on the observer's x and y values,
	// and scales in x and y relative to the negative of the observer's z value
	// (the observer is in the negative z direction).

	orien->set(SkMatrix::kMScaleX, x * axis.fX - z * cross.fX);
	orien->set(SkMatrix::kMSkewX, x * axis.fY - z * cross.fY);
	orien->set(SkMatrix::kMTransX, x * axis.fZ - z * cross.fZ);
	orien->set(SkMatrix::kMSkewY, y * axis.fX - z * zenith.fX);
	orien->set(SkMatrix::kMScaleY, y * axis.fY - z * zenith.fY);
	orien->set(SkMatrix::kMTransY, y * axis.fZ - z * zenith.fZ);
	orien->set(SkMatrix::kMPersp0, axis.fX);
	orien->set(SkMatrix::kMPersp1, axis.fY);
	orien->set(SkMatrix::kMPersp2, axis.fZ);
	}
	}

	void SkCamera3D::patchToMatrix(const SkPatch3D& quilt, SkMatrix* matrix) const {
	if (fNeedToUpdate) {
	this->doUpdate();
	fNeedToUpdate = false;
	}

	const SkScalar* mapPtr = (const SkScalar)(const void)&fOrientation;
	const SkScalar* patchPtr;
	SkPoint3D diff;
	SkScalar dot;

	diff.fX = quilt.fOrigin.fX - fLocation.fX;
	diff.fY = quilt.fOrigin.fY - fLocation.fY;
	diff.fZ = quilt.fOrigin.fZ - fLocation.fZ;

	dot = SkUnit3D::Dot(SkUnit3D{diff.fX, diff.fY, diff.fZ},
	SkUnit3D{mapPtr[6], mapPtr[7], mapPtr[8]});

	// This multiplies fOrientation by the matrix [quilt.fU quilt.fV diff] -- U, V, and diff are
	// column vectors in the matrix -- then divides by the length of the projection of diff onto
	// the view axis (which is 'dot'). This transforms the patch (which transforms from local path
	// space to world space) into view space (since fOrientation transforms from world space to
	// view space).
	//
	// The divide by 'dot' isn't strictly necessary as the homogeneous divide would do much the
	// same thing (it's just scaling the entire matrix by 1/dot). It looks like it's normalizing
	// the matrix into some canonical space.
	patchPtr = (const SkScalar*)&quilt;
	matrix->set(SkMatrix::kMScaleX, SkScalarDotDiv(3, patchPtr, 1, mapPtr, 1, dot));
	matrix->set(SkMatrix::kMSkewY, SkScalarDotDiv(3, patchPtr, 1, mapPtr+3, 1, dot));
	matrix->set(SkMatrix::kMPersp0, SkScalarDotDiv(3, patchPtr, 1, mapPtr+6, 1, dot));

	patchPtr += 3;
	matrix->set(SkMatrix::kMSkewX, SkScalarDotDiv(3, patchPtr, 1, mapPtr, 1, dot));
	matrix->set(SkMatrix::kMScaleY, SkScalarDotDiv(3, patchPtr, 1, mapPtr+3, 1, dot));
	matrix->set(SkMatrix::kMPersp1, SkScalarDotDiv(3, patchPtr, 1, mapPtr+6, 1, dot));

	patchPtr = (const SkScalar)(const void)&diff;
	matrix->set(SkMatrix::kMTransX, SkScalarDotDiv(3, patchPtr, 1, mapPtr, 1, dot));
	matrix->set(SkMatrix::kMTransY, SkScalarDotDiv(3, patchPtr, 1, mapPtr+3, 1, dot));
	matrix->set(SkMatrix::kMPersp2, SK_Scalar1);
	}

	///////////////////////////////////////////////////////////////////////////////

	Sk3DView::Sk3DView() {
	fInitialRec.fMatrix.reset();
	fRec = &fInitialRec;
	}

	Sk3DView::~Sk3DView() {
	Rec* rec = fRec;
	while (rec != &fInitialRec) {
	Rec* next = rec->fNext;
	delete rec;
	rec = next;
	}
	}

	void Sk3DView::save() {
	Rec* rec = new Rec;
	rec->fNext = fRec;
	rec->fMatrix = fRec->fMatrix;
	fRec = rec;
	}

	void Sk3DView::restore() {
	SkASSERT(fRec != &fInitialRec);
	Rec* next = fRec->fNext;
	delete fRec;
	fRec = next;
	}

	#ifdef SK_BUILD_FOR_ANDROID
	void Sk3DView::setCameraLocation(SkScalar x, SkScalar y, SkScalar z) {
	// the camera location is passed in inches, set in pt
	SkScalar lz = z * 72.0f;
	fCamera.fLocation.set(x * 72.0f, y * 72.0f, lz);
	fCamera.fObserver.set(0, 0, lz);
	fCamera.update();

	}

	SkScalar Sk3DView::getCameraLocationX() {
	return fCamera.fLocation.fX / 72.0f;
	}

	SkScalar Sk3DView::getCameraLocationY() {
	return fCamera.fLocation.fY / 72.0f;
	}

	SkScalar Sk3DView::getCameraLocationZ() {
	return fCamera.fLocation.fZ / 72.0f;
	}
	#endif

	void Sk3DView::translate(SkScalar x, SkScalar y, SkScalar z) {
	fRec->fMatrix.preTranslate(x, y, z);
	}

	void Sk3DView::rotateX(SkScalar deg) {
	fRec->fMatrix.preRotateX(deg);
	}

	void Sk3DView::rotateY(SkScalar deg) {
	fRec->fMatrix.preRotateY(deg);
	}

	void Sk3DView::rotateZ(SkScalar deg) {
	fRec->fMatrix.preRotateZ(deg);
	}

	SkScalar Sk3DView::dotWithNormal(SkScalar x, SkScalar y, SkScalar z) const {
	SkPatch3D patch;
	patch.transform(fRec->fMatrix);
	return patch.dotWith(x, y, z);
	}

	void Sk3DView::getMatrix(SkMatrix* matrix) const {
	if (matrix != nullptr) {
	SkPatch3D patch;
	patch.transform(fRec->fMatrix);
	fCamera.patchToMatrix(patch, matrix);
	}
	}

	#include "SkCanvas.h"

	void Sk3DView::applyToCanvas(SkCanvas* canvas) const {
	SkMatrix matrix;

	this->getMatrix(&matrix);
	canvas->concat(matrix);
	}