summaryrefslogtreecommitdiffstats
path: root/gfx/2d/Polygon.h
diff options
context:
space:
mode:
Diffstat (limited to '')
-rw-r--r--gfx/2d/Polygon.h396
1 files changed, 396 insertions, 0 deletions
diff --git a/gfx/2d/Polygon.h b/gfx/2d/Polygon.h
new file mode 100644
index 0000000000..3de3d684f9
--- /dev/null
+++ b/gfx/2d/Polygon.h
@@ -0,0 +1,396 @@
+/* -*- 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/. */
+
+#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.
+ // http://mathworld.wolfram.com/Point-PlaneDistance.html
+ 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 */