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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
#ifndef MOZILLA_GFX_POLYGON_H
#define MOZILLA_GFX_POLYGON_H
#include <initializer_list>
#include <utility>
#include "Matrix.h"
#include "Point.h"
#include "Triangle.h"
#include "nsTArray.h"
namespace mozilla {
namespace gfx {
/**
* Calculates the w = 0 intersection point for the edge defined by
* |aFirst| and |aSecond|.
*/
template <class Units>
Point4DTyped<Units> CalculateEdgeIntersect(const Point4DTyped<Units>& aFirst,
const Point4DTyped<Units>& aSecond) {
static const float w = 0.00001f;
const float t = (w - aFirst.w) / (aSecond.w - aFirst.w);
return aFirst + (aSecond - aFirst) * t;
}
/**
* Clips the polygon defined by |aPoints| so that there are no points with
* w <= 0.
*/
template <class Units>
nsTArray<Point4DTyped<Units>> ClipPointsAtInfinity(
const nsTArray<Point4DTyped<Units>>& aPoints) {
nsTArray<Point4DTyped<Units>> outPoints(aPoints.Length());
const size_t pointCount = aPoints.Length();
for (size_t i = 0; i < pointCount; ++i) {
const Point4DTyped<Units>& first = aPoints[i];
const Point4DTyped<Units>& second = aPoints[(i + 1) % pointCount];
if (!first.w || !second.w) {
// Skip edges at infinity.
continue;
}
if (first.w > 0.0f) {
outPoints.AppendElement(first);
}
if ((first.w <= 0.0f) ^ (second.w <= 0.0f)) {
outPoints.AppendElement(CalculateEdgeIntersect(first, second));
}
}
return outPoints;
}
/**
* Calculates the distances between the points in |aPoints| and the plane
* defined by |aPlaneNormal| and |aPlanePoint|.
*/
template <class Units>
nsTArray<float> CalculatePointPlaneDistances(
const nsTArray<Point4DTyped<Units>>& aPoints,
const Point4DTyped<Units>& aPlaneNormal,
const Point4DTyped<Units>& aPlanePoint, size_t& aPos, size_t& aNeg) {
// Point classification might produce incorrect results due to numerical
// inaccuracies. Using an epsilon value makes the splitting plane "thicker".
const float epsilon = 0.05f;
aPos = aNeg = 0;
nsTArray<float> distances(aPoints.Length());
for (const Point4DTyped<Units>& point : aPoints) {
float dot = (point - aPlanePoint).DotProduct(aPlaneNormal);
if (dot > epsilon) {
aPos++;
} else if (dot < -epsilon) {
aNeg++;
} else {
// The point is within the thick plane.
dot = 0.0f;
}
distances.AppendElement(dot);
}
return distances;
}
/**
* Clips the polygon defined by |aPoints|. The clipping uses previously
* calculated plane to point distances and the plane normal |aNormal|.
* The result of clipping is stored in |aBackPoints| and |aFrontPoints|.
*/
template <class Units>
void ClipPointsWithPlane(const nsTArray<Point4DTyped<Units>>& aPoints,
const Point4DTyped<Units>& aNormal,
const nsTArray<float>& aDots,
nsTArray<Point4DTyped<Units>>& aBackPoints,
nsTArray<Point4DTyped<Units>>& aFrontPoints) {
static const auto Sign = [](const float& f) {
if (f > 0.0f) return 1;
if (f < 0.0f) return -1;
return 0;
};
const size_t pointCount = aPoints.Length();
for (size_t i = 0; i < pointCount; ++i) {
size_t j = (i + 1) % pointCount;
const Point4DTyped<Units>& a = aPoints[i];
const Point4DTyped<Units>& b = aPoints[j];
const float dotA = aDots[i];
const float dotB = aDots[j];
// The point is in front of or on the plane.
if (dotA >= 0) {
aFrontPoints.AppendElement(a);
}
// The point is behind or on the plane.
if (dotA <= 0) {
aBackPoints.AppendElement(a);
}
// If the sign of the dot products changes between two consecutive
// vertices, then the plane intersects with the polygon edge.
// The case where the polygon edge is within the plane is handled above.
if (Sign(dotA) && Sign(dotB) && Sign(dotA) != Sign(dotB)) {
// Calculate the line segment and plane intersection point.
const Point4DTyped<Units> ab = b - a;
const float dotAB = ab.DotProduct(aNormal);
const float t = -dotA / dotAB;
const Point4DTyped<Units> p = a + (ab * t);
// Add the intersection point to both polygons.
aBackPoints.AppendElement(p);
aFrontPoints.AppendElement(p);
}
}
}
/**
* PolygonTyped stores the points of a convex planar polygon.
*/
template <class Units>
class PolygonTyped {
typedef Point3DTyped<Units> Point3DType;
typedef Point4DTyped<Units> Point4DType;
public:
PolygonTyped() = default;
explicit PolygonTyped(const nsTArray<Point4DType>& aPoints,
const Point4DType& aNormal = DefaultNormal())
: mNormal(aNormal), mPoints(aPoints) {}
explicit PolygonTyped(nsTArray<Point4DType>&& aPoints,
const Point4DType& aNormal = DefaultNormal())
: mNormal(aNormal), mPoints(std::move(aPoints)) {}
explicit PolygonTyped(const std::initializer_list<Point4DType>& aPoints,
const Point4DType& aNormal = DefaultNormal())
: mNormal(aNormal), mPoints(aPoints) {
#ifdef DEBUG
EnsurePlanarPolygon();
#endif
}
/**
* Returns the smallest 2D rectangle that can fully cover the polygon.
*/
RectTyped<Units> BoundingBox() const {
if (mPoints.IsEmpty()) {
return RectTyped<Units>();
}
float minX, maxX, minY, maxY;
minX = maxX = mPoints[0].x;
minY = maxY = mPoints[0].y;
for (const Point4DType& point : mPoints) {
minX = std::min(point.x, minX);
maxX = std::max(point.x, maxX);
minY = std::min(point.y, minY);
maxY = std::max(point.y, maxY);
}
return RectTyped<Units>(minX, minY, maxX - minX, maxY - minY);
}
/**
* Clips the polygon against the given 2D rectangle.
*/
PolygonTyped<Units> ClipPolygon(const RectTyped<Units>& aRect) const {
if (aRect.IsEmpty()) {
return PolygonTyped<Units>();
}
return ClipPolygon(FromRect(aRect));
}
/**
* Clips this polygon against |aPolygon| in 2D and returns a new polygon.
*/
PolygonTyped<Units> ClipPolygon(const PolygonTyped<Units>& aPolygon) const {
const nsTArray<Point4DType>& points = aPolygon.GetPoints();
if (mPoints.IsEmpty() || points.IsEmpty()) {
return PolygonTyped<Units>();
}
nsTArray<Point4DType> clippedPoints(mPoints.Clone());
size_t pos, neg;
nsTArray<Point4DType> backPoints(4), frontPoints(4);
// Iterate over all the edges of the clipping polygon |aPolygon| and clip
// this polygon against the edges.
const size_t pointCount = points.Length();
for (size_t i = 0; i < pointCount; ++i) {
const Point4DType p1 = points[(i + 1) % pointCount];
const Point4DType p2 = points[i];
// Calculate the normal for the edge defined by |p1| and |p2|.
const Point4DType normal(p2.y - p1.y, p1.x - p2.x, 0.0f, 0.0f);
// Calculate the distances between the points of the polygon and the
// plane defined by |aPolygon|.
const nsTArray<float> distances =
CalculatePointPlaneDistances(clippedPoints, normal, p1, pos, neg);
backPoints.ClearAndRetainStorage();
frontPoints.ClearAndRetainStorage();
// Clip the polygon points using the previously calculated distances.
ClipPointsWithPlane(clippedPoints, normal, distances, backPoints,
frontPoints);
// Only use the points behind the clipping plane.
clippedPoints = std::move(backPoints);
if (clippedPoints.Length() < 3) {
// The clipping created a polygon with no area.
return PolygonTyped<Units>();
}
}
return PolygonTyped<Units>(std::move(clippedPoints), mNormal);
}
/**
* Returns a new polygon containing the bounds of the given 2D rectangle.
*/
static PolygonTyped<Units> FromRect(const RectTyped<Units>& aRect) {
nsTArray<Point4DType> points{
Point4DType(aRect.X(), aRect.Y(), 0.0f, 1.0f),
Point4DType(aRect.X(), aRect.YMost(), 0.0f, 1.0f),
Point4DType(aRect.XMost(), aRect.YMost(), 0.0f, 1.0f),
Point4DType(aRect.XMost(), aRect.Y(), 0.0f, 1.0f)};
return PolygonTyped<Units>(std::move(points));
}
const Point4DType& GetNormal() const { return mNormal; }
const nsTArray<Point4DType>& GetPoints() const { return mPoints; }
bool IsEmpty() const {
// If the polygon has less than three points, it has no visible area.
return mPoints.Length() < 3;
}
/**
* Returns a list of triangles covering the polygon.
*/
nsTArray<TriangleTyped<Units>> ToTriangles() const {
nsTArray<TriangleTyped<Units>> triangles;
if (IsEmpty()) {
return triangles;
}
// This fan triangulation method only works for convex polygons.
for (size_t i = 1; i < mPoints.Length() - 1; ++i) {
TriangleTyped<Units> triangle(Point(mPoints[0].x, mPoints[0].y),
Point(mPoints[i].x, mPoints[i].y),
Point(mPoints[i + 1].x, mPoints[i + 1].y));
triangles.AppendElement(std::move(triangle));
}
return triangles;
}
void TransformToLayerSpace(const Matrix4x4Typed<Units, Units>& aTransform) {
TransformPoints(aTransform, true);
mNormal = DefaultNormal();
}
void TransformToScreenSpace(
const Matrix4x4Typed<Units, Units>& aTransform,
const Matrix4x4Typed<Units, Units>& aInverseTransform) {
TransformPoints(aTransform, false);
// Perspective projection transformation might produce points with w <= 0,
// so we need to clip these points.
mPoints = ClipPointsAtInfinity(mPoints);
// Normal vectors should be transformed using inverse transpose.
mNormal = aInverseTransform.TransposeTransform4D(mNormal);
}
void TransformToScreenSpace(const Matrix4x4Typed<Units, Units>& aTransform) {
MOZ_ASSERT(!aTransform.IsSingular());
TransformToScreenSpace(aTransform, aTransform.Inverse());
}
private:
static Point4DType DefaultNormal() {
return Point4DType(0.0f, 0.0f, 1.0f, 0.0f);
}
#ifdef DEBUG
void EnsurePlanarPolygon() const {
if (mPoints.Length() <= 3) {
// Polygons with three or less points are guaranteed to be planar.
return;
}
// This normal calculation method works only for planar polygons.
// The resulting normal vector will point towards the viewer when the
// polygon has a counter-clockwise winding order from the perspective
// of the viewer.
Point3DType normal;
const Point3DType p0 = mPoints[0].As3DPoint();
for (size_t i = 1; i < mPoints.Length() - 1; ++i) {
const Point3DType p1 = mPoints[i].As3DPoint();
const Point3DType p2 = mPoints[i + 1].As3DPoint();
normal += (p1 - p0).CrossProduct(p2 - p0);
}
// Ensure that at least one component is greater than zero.
// This avoids division by zero when normalizing the vector.
bool hasNonZeroComponent = std::abs(normal.x) > 0.0f ||
std::abs(normal.y) > 0.0f ||
std::abs(normal.z) > 0.0f;
MOZ_ASSERT(hasNonZeroComponent);
normal.Normalize();
// Ensure that the polygon is planar.
const float epsilon = 0.01f;
for (const Point4DType& point : mPoints) {
const Point3DType p1 = point.As3DPoint();
const float d = normal.DotProduct(p1 - p0);
MOZ_ASSERT(std::abs(d) < epsilon);
}
}
#endif
void TransformPoints(const Matrix4x4Typed<Units, Units>& aTransform,
const bool aDivideByW) {
for (Point4DType& point : mPoints) {
point = aTransform.TransformPoint(point);
if (aDivideByW && point.w > 0.0f) {
point = point / point.w;
}
}
}
Point4DType mNormal;
CopyableTArray<Point4DType> mPoints;
};
typedef PolygonTyped<UnknownUnits> Polygon;
} // namespace gfx
} // namespace mozilla
#endif /* MOZILLA_GFX_POLYGON_H */