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187 lines
5.4 KiB
C++
187 lines
5.4 KiB
C++
/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
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/* vim: set ts=8 sts=2 et sw=2 tw=80: */
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/* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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#ifndef mozilla_BezierUtils_h_
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#define mozilla_BezierUtils_h_
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#include "mozilla/gfx/Point.h"
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#include "mozilla/gfx/Types.h"
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namespace mozilla {
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namespace gfx {
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// Control points for bezier curve
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//
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// mPoints[2]
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// +-----___---+ mPoints[3]
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// __--
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// _--
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// /
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// /
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// mPoints[1] + |
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// | |
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// ||
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// ||
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// |
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// |
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// |
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// |
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// mPoints[0] +
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struct Bezier {
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Point mPoints[4];
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};
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// Calculate a point or it's differential of a bezier curve formed by
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// aBezier and parameter t.
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//
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// GetBezierPoint = P(t)
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// GetBezierDifferential = P'(t)
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// GetBezierDifferential2 = P''(t)
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//
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// mPoints[2]
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// +-----___---+ mPoints[3]
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// __-- P(1)
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// _--
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// +
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// / P(t)
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// mPoints[1] + |
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// | |
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// ||
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// ||
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// |
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// |
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// |
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// |
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// mPoints[0] + P(0)
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Point GetBezierPoint(const Bezier& aBezier, Float t);
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Point GetBezierDifferential(const Bezier& aBezier, Float t);
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Point GetBezierDifferential2(const Bezier& aBezier, Float t);
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// Calculate length of a simple bezier curve formed by aBezier and range [a, b].
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Float GetBezierLength(const Bezier& aBezier, Float a, Float b);
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// Split bezier curve formed by aBezier into [0,t1], [t1,t2], [t2,1] parts, and
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// stores control points for [t1,t2] to aSubBezier.
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//
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// ___---+
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// __+- P(1)
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// _-- P(t2)
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// -
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// / <-- aSubBezier
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// |
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// |
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// +
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// | P(t1)
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// |
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// |
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// |
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// |
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// + P(0)
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void GetSubBezier(Bezier* aSubBezier, const Bezier& aBezier, Float t1,
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Float t2);
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// Find a nearest point on bezier curve formed by aBezier to a point aTarget.
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// aInitialT is a hint to find the parameter t for the nearest point.
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// If aT is non-null, parameter for the nearest point is stored to *aT.
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// This function expects a bezier curve to be an approximation of elliptic arc.
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// Otherwise it will return wrong point.
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//
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// aTarget
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// + ___---+
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// __--
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// _--
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// +
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// / nearest point = P(t = *aT)
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// |
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// |
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// |
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// + P(aInitialT)
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// |
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// |
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// |
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// |
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// +
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Point FindBezierNearestPoint(const Bezier& aBezier, const Point& aTarget,
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Float aInitialT, Float* aT = nullptr);
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// Calculate control points for a bezier curve that is an approximation of
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// an elliptic arc.
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//
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// aCornerSize.width
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// |<----------------->|
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// | |
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// aCornerPoint| mPoints[2] |
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// -------------+-------+-----___---+ mPoints[3]
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// ^ | __--
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// | | _--
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// | | -
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// | | /
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// aCornerSize.height | mPoints[1] + |
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// | | |
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// | ||
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// | ||
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// | |
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// | |
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// | |
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// v mPoints[0] |
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// -------------+
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void GetBezierPointsForCorner(Bezier* aBezier, mozilla::Corner aCorner,
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const Point& aCornerPoint,
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const Size& aCornerSize);
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// Calculate the approximate length of a quarter elliptic arc formed by radii
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// (a, b).
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//
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// a
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// |<----------------->|
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// | |
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// ---+-------------___---+
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// ^ | __--
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// | | _--
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// | | -
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// | | /
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// b | | |
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// | | |
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// | ||
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// | ||
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// | |
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// | |
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// | |
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// v |
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// ---+
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Float GetQuarterEllipticArcLength(Float a, Float b);
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// Calculate the distance between an elliptic arc formed by (origin, width,
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// height), and a point P, along a line formed by |P + n * normal|.
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// P should be outside of the ellipse, and the line should cross with the
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// ellipse twice at n > 0 points.
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//
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// width
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// |<----------------->|
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// origin | |
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// -----------+-------------___---+
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// ^ normal | __--
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// | P +->__ | _--
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// | --__ -
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// | | --+
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// height | | |
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// | | |
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// | ||
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// | ||
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// | |
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// | |
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// | |
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// v |
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// -----------+
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Float CalculateDistanceToEllipticArc(const Point& P, const Point& normal,
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const Point& origin, Float width,
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Float height);
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} // namespace gfx
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} // namespace mozilla
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#endif /* mozilla_BezierUtils_h_ */
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