Aegisub/src/spline_curve.cpp

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// Copyright (c) 2007, Rodrigo Braz Monteiro
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of the Aegisub Group nor the names of its contributors
// may be used to endorse or promote products derived from this software
// without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Aegisub Project http://www.aegisub.org/
/// @file spline_curve.cpp
/// @brief Handle bicubic splines (Bezier curves) in vector drawings
/// @ingroup visual_ts
///
#include "spline_curve.h"
#include "utils.h"
#include <limits>
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SplineCurve::SplineCurve(Vector2D p1) : p1(p1), type(POINT) { }
SplineCurve::SplineCurve(Vector2D p1, Vector2D p2) : p1(p1), p2(p2), type(LINE) { }
SplineCurve::SplineCurve(Vector2D p1, Vector2D p2, Vector2D p3, Vector2D p4)
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: p1(p1), p2(p2), p3(p3), p4(p4), type(BICUBIC)
{
}
std::pair<SplineCurve, SplineCurve> SplineCurve::Split(float t) {
if (type == LINE) {
Vector2D m = p1 * (1 - t) + p2 * t;
return {
SplineCurve(p1, m),
SplineCurve(m, p2)
};
}
else if (type == BICUBIC) {
float u = 1 - t;
Vector2D p12 = p1 * u + p2 * t;
Vector2D p23 = p2 * u + p3 * t;
Vector2D p34 = p3 * u + p4 * t;
Vector2D p123 = p12 * u + p23 * t;
Vector2D p234 = p23 * u + p34 * t;
Vector2D p1234 = p123 * u + p234 * t;
return {
SplineCurve(p1, p12, p123, p1234),
SplineCurve(p1234, p234, p34, p4)
};
}
return {SplineCurve(p1), SplineCurve(p1)};
}
void SplineCurve::Smooth(Vector2D p0, Vector2D p5, float smooth) {
if (type != LINE || p1 == p2) return;
smooth = mid(0.f, smooth, 1.f);
// Calculate intermediate points
Vector2D c1 = (p0 + p1) / 2.f;
Vector2D c2 = (p1 + p2) / 2.f;
Vector2D c3 = (p2 + p5) / 2.f;
float len1 = (p1 - p0).Len();
float len2 = (p2 - p1).Len();
float len3 = (p5 - p2).Len();
float k1 = len1 / (len1 + len2);
float k2 = len2 / (len2 + len3);
Vector2D m1 = c1 + (c2 - c1) * k1;
Vector2D m2 = c2 + (c3 - c2) * k2;
// Set curve points
p4 = p2;
p3 = m2 + (c2 - m2) * smooth + p2 - m2;
p2 = m1 + (c2 - m1) * smooth + p1 - m1;
type = BICUBIC;
}
Vector2D SplineCurve::GetPoint(float t) const {
float u = 1.f - t;
if (type == POINT)
return p1;
if (type == LINE)
return p1 * u + p2 * t;
return p1*u*u*u + 3*p2*t*u*u + 3*p3*t*t*u + p4*t*t*t;
}
Vector2D& SplineCurve::EndPoint() {
switch (type) {
case POINT: return p1;
case LINE: return p2;
case BICUBIC: return p4;
default: return p1;
}
}
Vector2D SplineCurve::GetClosestPoint(Vector2D ref) const {
return GetPoint(GetClosestParam(ref));
}
float SplineCurve::GetClosestParam(Vector2D ref) const {
if (type == LINE)
return GetClosestSegmentPart(p1, p2, ref);
if (type == BICUBIC) {
int steps = 100;
float bestDist = std::numeric_limits<float>::max();
float bestT = 0.f;
for (int i = 0; i <= steps; ++i) {
float t = i / float(steps);
float dist = (GetPoint(t) - ref).SquareLen();
if (dist < bestDist) {
bestDist = dist;
bestT = t;
}
}
return bestT;
}
return 0.f;
}
float SplineCurve::GetQuickDistance(Vector2D ref) const {
if (type == BICUBIC) {
float lens[] = {
GetClosestSegmentDistance(p1, p2, ref),
GetClosestSegmentDistance(p2, p3, ref),
GetClosestSegmentDistance(p3, p4, ref),
GetClosestSegmentDistance(p4, p1, ref),
GetClosestSegmentDistance(p1, p3, ref),
GetClosestSegmentDistance(p2, p4, ref)
};
return *std::min_element(lens, lens + 6);
}
return (GetClosestPoint(ref) - ref).Len();
}
float SplineCurve::GetClosestSegmentPart(Vector2D pt1, Vector2D pt2, Vector2D pt3) const {
return mid(0.f, (pt3 - pt1).Dot(pt2 - pt1) / (pt2 - pt1).SquareLen(), 1.f);
}
float SplineCurve::GetClosestSegmentDistance(Vector2D pt1, Vector2D pt2, Vector2D pt3) const {
float t = GetClosestSegmentPart(pt1, pt2, pt3);
return (pt1 * (1.f - t) + pt2 * t - pt3).Len();
}
int SplineCurve::GetPoints(std::vector<float> &points) const {
switch (type) {
case POINT:
points.push_back(p1.X());
points.push_back(p1.Y());
return 1;
case LINE:
points.push_back(p2.X());
points.push_back(p2.Y());
return 1;
case BICUBIC: {
int len = int(
(p2 - p1).Len() +
(p3 - p2).Len() +
(p4 - p3).Len());
int steps = len/8;
for (int i = 0; i <= steps; ++i) {
// Get t and t-1 (u)
float t = i / float(steps);
Vector2D p = GetPoint(t);
points.push_back(p.X());
points.push_back(p.Y());
}
return steps + 1;
}
default:
return 0;
}
}