gecko-dev/gfx/2d/Polygon.h

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/* -*- Mode: C++; tab-width: 2; 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/. */
#ifndef MOZILLA_GFX_POLYGON_H
#define MOZILLA_GFX_POLYGON_H
#include "Matrix.h"
#include "mozilla/Move.h"
#include "nsTArray.h"
#include "Point.h"
#include "Triangle.h"
#include <initializer_list>
namespace mozilla {
namespace gfx {
// Polygon3DTyped stores the points of a convex planar polygon.
template<class Units>
class Polygon3DTyped {
public:
Polygon3DTyped() {}
explicit Polygon3DTyped(const std::initializer_list<Point3DTyped<Units>>& aPoints,
Point3DTyped<Units> aNormal =
Point3DTyped<Units>(0.0f, 0.0f, 1.0f))
: mNormal(aNormal), mPoints(aPoints)
{
#ifdef DEBUG
EnsurePlanarPolygon();
#endif
}
explicit Polygon3DTyped(nsTArray<Point3DTyped<Units>>&& aPoints,
Point3DTyped<Units> aNormal =
Point3DTyped<Units>(0.0f, 0.0f, 1.0f))
: mNormal(aNormal), mPoints(Move(aPoints))
{
#ifdef DEBUG
EnsurePlanarPolygon();
#endif
}
explicit Polygon3DTyped(const nsTArray<Point3DTyped<Units>>& aPoints,
Point3DTyped<Units> aNormal =
Point3DTyped<Units>(0.0f, 0.0f, 1.0f))
: mNormal(aNormal), mPoints(aPoints)
{
#ifdef DEBUG
EnsurePlanarPolygon();
#endif
}
RectTyped<Units> BoundingBox() const
{
float minX, maxX, minY, maxY;
minX = maxX = mPoints[0].x;
minY = maxY = mPoints[0].y;
for (const Point3DTyped<Units>& 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);
}
nsTArray<float>
CalculateDotProducts(const Polygon3DTyped<Units>& aPlane,
size_t& aPos, size_t& aNeg) const
{
// Point classification might produce incorrect results due to numerical
// inaccuracies. Using an epsilon value makes the splitting plane "thicker".
const float epsilon = 0.05f;
MOZ_ASSERT(!aPlane.GetPoints().IsEmpty());
const Point3DTyped<Units>& planeNormal = aPlane.GetNormal();
const Point3DTyped<Units>& planePoint = aPlane[0];
aPos = aNeg = 0;
nsTArray<float> dotProducts;
for (const Point3DTyped<Units>& point : mPoints) {
float dot = (point - planePoint).DotProduct(planeNormal);
if (dot > epsilon) {
aPos++;
} else if (dot < -epsilon) {
aNeg++;
} else {
// The point is within the thick plane.
dot = 0.0f;
}
dotProducts.AppendElement(dot);
}
return dotProducts;
}
// Clips the polygon against the given 2D rectangle.
Polygon3DTyped<Units> ClipPolygon(const RectTyped<Units>& aRect) const
{
Polygon3DTyped<Units> polygon(mPoints, mNormal);
// Left edge
ClipPolygonWithEdge(polygon, aRect.BottomLeft(), aRect.TopLeft());
// Bottom edge
ClipPolygonWithEdge(polygon, aRect.BottomRight(), aRect.BottomLeft());
// Right edge
ClipPolygonWithEdge(polygon, aRect.TopRight(), aRect.BottomRight());
// Top edge
ClipPolygonWithEdge(polygon, aRect.TopLeft(), aRect.TopRight());
return polygon;
}
const Point3DTyped<Units>& GetNormal() const
{
return mNormal;
}
const nsTArray<Point3DTyped<Units>>& GetPoints() const
{
return mPoints;
}
const Point3DTyped<Units>& operator[](size_t aIndex) const
{
MOZ_ASSERT(mPoints.Length() > aIndex);
return mPoints[aIndex];
}
void SplitPolygon(const Polygon3DTyped<Units>& aSplittingPlane,
const nsTArray<float>& aDots,
nsTArray<Point3DTyped<Units>>& aBackPoints,
nsTArray<Point3DTyped<Units>>& aFrontPoints) const
{
static const auto Sign = [](const float& f) {
if (f > 0.0f) return 1;
if (f < 0.0f) return -1;
return 0;
};
const Point3DTyped<Units>& normal = aSplittingPlane.GetNormal();
const size_t pointCount = mPoints.Length();
for (size_t i = 0; i < pointCount; ++i) {
size_t j = (i + 1) % pointCount;
const Point3DTyped<Units>& a = mPoints[i];
const Point3DTyped<Units>& b = mPoints[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 Point3DTyped<Units> ab = b - a;
const float dotAB = ab.DotProduct(normal);
const float t = -dotA / dotAB;
const Point3DTyped<Units> p = a + (ab * t);
// Add the intersection point to both polygons.
aBackPoints.AppendElement(p);
aFrontPoints.AppendElement(p);
}
}
}
nsTArray<TriangleTyped<Units>> ToTriangles() const
{
nsTArray<TriangleTyped<Units>> triangles;
if (mPoints.Length() < 3) {
return triangles;
}
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(Move(triangle));
}
return triangles;
}
void TransformToLayerSpace(const Matrix4x4Typed<Units, Units>& aTransform)
{
TransformPoints(aTransform);
mNormal = Point3DTyped<Units>(0.0f, 0.0f, 1.0f);
}
void TransformToScreenSpace(const Matrix4x4Typed<Units, Units>& aTransform)
{
TransformPoints(aTransform);
// Normal vectors should be transformed using inverse transpose.
mNormal = aTransform.Inverse().Transpose().TransformPoint(mNormal);
}
private:
void ClipPolygonWithEdge(Polygon3DTyped<Units>& aPolygon,
const PointTyped<Units>& aFirst,
const PointTyped<Units>& aSecond) const
{
const Point3DTyped<Units> a(aFirst.x, aFirst.y, 0.0f);
const Point3DTyped<Units> b(aSecond.x, aSecond.y, 0.0f);
const Point3DTyped<Units> normal(b.y - a.y, a.x - b.x, 0.0f);
Polygon3DTyped<Units> plane({a, b}, normal);
size_t pos, neg;
nsTArray<float> dots = aPolygon.CalculateDotProducts(plane, pos, neg);
nsTArray<Point3DTyped<Units>> backPoints, frontPoints;
aPolygon.SplitPolygon(plane, dots, backPoints, frontPoints);
// Only use the points that are behind the clipping plane.
aPolygon = Polygon3DTyped<Units>(Move(backPoints), aPolygon.GetNormal());
}
#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.
Point3DTyped<Units> normal;
for (size_t i = 1; i < mPoints.Length() - 1; ++i) {
normal +=
(mPoints[i] - mPoints[0]).CrossProduct(mPoints[i + 1] - mPoints[0]);
}
// 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 Point3DTyped<Units>& point : mPoints) {
float d = normal.DotProduct(point - mPoints[0]);
MOZ_ASSERT(std::abs(d) < epsilon);
}
}
#endif
void TransformPoints(const Matrix4x4Typed<Units, Units>& aTransform)
{
for (Point3DTyped<Units>& point : mPoints) {
point = aTransform.TransformPoint(point);
}
}
Point3DTyped<Units> mNormal;
nsTArray<Point3DTyped<Units>> mPoints;
};
typedef Polygon3DTyped<UnknownUnits> Polygon3D;
} // namespace gfx
} // namespace mozilla
#endif /* MOZILLA_GFX_POLYGON_H */