/*
* Copyright (c) 2020 - 2024 the ThorVG project. All rights reserved.
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "tvgMath.h"
#include "tvgBezier.h"
#define BEZIER_EPSILON 1e-4f
/************************************************************************/
/* Internal Class Implementation */
/************************************************************************/
static float _lineLengthApprox(const Point& pt1, const Point& pt2)
{
/* approximate sqrt(x*x + y*y) using alpha max plus beta min algorithm.
With alpha = 1, beta = 3/8, giving results with the largest error less
than 7% compared to the exact value. */
Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};
if (diff.x < 0) diff.x = -diff.x;
if (diff.y < 0) diff.y = -diff.y;
return (diff.x > diff.y) ? (diff.x + diff.y * 0.375f) : (diff.y + diff.x * 0.375f);
}
static float _lineLength(const Point& pt1, const Point& pt2)
{
Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};
return sqrtf(diff.x * diff.x + diff.y * diff.y);
}
template<typename LengthFunc>
float _bezLength(const Bezier& cur, LengthFunc lineLengthFunc)
{
Bezier left, right;
auto len = lineLengthFunc(cur.start, cur.ctrl1) + lineLengthFunc(cur.ctrl1, cur.ctrl2) + lineLengthFunc(cur.ctrl2, cur.end);
auto chord = lineLengthFunc(cur.start, cur.end);
if (fabsf(len - chord) > BEZIER_EPSILON) {
tvg::bezSplit(cur, left, right);
return _bezLength(left, lineLengthFunc) + _bezLength(right, lineLengthFunc);
}
return len;
}
template<typename LengthFunc>
float _bezAt(const Bezier& bz, float at, float length, LengthFunc lineLengthFunc)
{
auto biggest = 1.0f;
auto smallest = 0.0f;
auto t = 0.5f;
//just in case to prevent an infinite loop
if (at <= 0) return 0.0f;
if (at >= length) return 1.0f;
while (true) {
auto right = bz;
Bezier left;
bezSplitLeft(right, t, left);
length = _bezLength(left, lineLengthFunc);
if (fabsf(length - at) < BEZIER_EPSILON || fabsf(smallest - biggest) < BEZIER_EPSILON) {
break;
}
if (length < at) {
smallest = t;
t = (t + biggest) * 0.5f;
} else {
biggest = t;
t = (smallest + t) * 0.5f;
}
}
return t;
}
/************************************************************************/
/* External Class Implementation */
/************************************************************************/
namespace tvg
{
void bezSplit(const Bezier& cur, Bezier& left, Bezier& right)
{
auto c = (cur.ctrl1.x + cur.ctrl2.x) * 0.5f;
left.ctrl1.x = (cur.start.x + cur.ctrl1.x) * 0.5f;
right.ctrl2.x = (cur.ctrl2.x + cur.end.x) * 0.5f;
left.start.x = cur.start.x;
right.end.x = cur.end.x;
left.ctrl2.x = (left.ctrl1.x + c) * 0.5f;
right.ctrl1.x = (right.ctrl2.x + c) * 0.5f;
left.end.x = right.start.x = (left.ctrl2.x + right.ctrl1.x) * 0.5f;
c = (cur.ctrl1.y + cur.ctrl2.y) * 0.5f;
left.ctrl1.y = (cur.start.y + cur.ctrl1.y) * 0.5f;
right.ctrl2.y = (cur.ctrl2.y + cur.end.y) * 0.5f;
left.start.y = cur.start.y;
right.end.y = cur.end.y;
left.ctrl2.y = (left.ctrl1.y + c) * 0.5f;
right.ctrl1.y = (right.ctrl2.y + c) * 0.5f;
left.end.y = right.start.y = (left.ctrl2.y + right.ctrl1.y) * 0.5f;
}
float bezLength(const Bezier& cur)
{
return _bezLength(cur, _lineLength);
}
float bezLengthApprox(const Bezier& cur)
{
return _bezLength(cur, _lineLengthApprox);
}
void bezSplitLeft(Bezier& cur, float at, Bezier& left)
{
left.start = cur.start;
left.ctrl1.x = cur.start.x + at * (cur.ctrl1.x - cur.start.x);
left.ctrl1.y = cur.start.y + at * (cur.ctrl1.y - cur.start.y);
left.ctrl2.x = cur.ctrl1.x + at * (cur.ctrl2.x - cur.ctrl1.x); //temporary holding spot
left.ctrl2.y = cur.ctrl1.y + at * (cur.ctrl2.y - cur.ctrl1.y); //temporary holding spot
cur.ctrl2.x = cur.ctrl2.x + at * (cur.end.x - cur.ctrl2.x);
cur.ctrl2.y = cur.ctrl2.y + at * (cur.end.y - cur.ctrl2.y);
cur.ctrl1.x = left.ctrl2.x + at * (cur.ctrl2.x - left.ctrl2.x);
cur.ctrl1.y = left.ctrl2.y + at * (cur.ctrl2.y - left.ctrl2.y);
left.ctrl2.x = left.ctrl1.x + at * (left.ctrl2.x - left.ctrl1.x);
left.ctrl2.y = left.ctrl1.y + at * (left.ctrl2.y - left.ctrl1.y);
left.end.x = cur.start.x = left.ctrl2.x + at * (cur.ctrl1.x - left.ctrl2.x);
left.end.y = cur.start.y = left.ctrl2.y + at * (cur.ctrl1.y - left.ctrl2.y);
}
float bezAt(const Bezier& bz, float at, float length)
{
return _bezAt(bz, at, length, _lineLength);
}
float bezAtApprox(const Bezier& bz, float at, float length)
{
return _bezAt(bz, at, length, _lineLengthApprox);
}
void bezSplitAt(const Bezier& cur, float at, Bezier& left, Bezier& right)
{
right = cur;
auto t = bezAt(right, at, bezLength(right));
bezSplitLeft(right, t, left);
}
Point bezPointAt(const Bezier& bz, float t)
{
Point cur;
auto it = 1.0f - t;
auto ax = bz.start.x * it + bz.ctrl1.x * t;
auto bx = bz.ctrl1.x * it + bz.ctrl2.x * t;
auto cx = bz.ctrl2.x * it + bz.end.x * t;
ax = ax * it + bx * t;
bx = bx * it + cx * t;
cur.x = ax * it + bx * t;
float ay = bz.start.y * it + bz.ctrl1.y * t;
float by = bz.ctrl1.y * it + bz.ctrl2.y * t;
float cy = bz.ctrl2.y * it + bz.end.y * t;
ay = ay * it + by * t;
by = by * it + cy * t;
cur.y = ay * it + by * t;
return cur;
}
float bezAngleAt(const Bezier& bz, float t)
{
if (t < 0 || t > 1) return 0;
//derivate
// p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 *
// t^2) * p2 + t^2 * p3)
float mt = 1.0f - t;
float d = t * t;
float a = -mt * mt;
float b = 1 - 4 * t + 3 * d;
float c = 2 * t - 3 * d;
Point pt ={a * bz.start.x + b * bz.ctrl1.x + c * bz.ctrl2.x + d * bz.end.x, a * bz.start.y + b * bz.ctrl1.y + c * bz.ctrl2.y + d * bz.end.y};
pt.x *= 3;
pt.y *= 3;
return atan2(pt.x, pt.y) * 180.0f / 3.141592f;
}
}