224 lines
6 KiB
C++
224 lines
6 KiB
C++
// Copyright (c) 2007, Rodrigo Braz Monteiro
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of the Aegisub Group nor the names of its contributors
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// may be used to endorse or promote products derived from this software
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// without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Aegisub Project http://www.aegisub.org/
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//
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// $Id$
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/// @file spline_curve.cpp
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/// @brief Handle bicubic splines (Bezier curves) in vector drawings
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/// @ingroup visual_ts
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///
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///////////
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// Headers
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#include "config.h"
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#include "spline_curve.h"
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#include "utils.h"
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/// @brief Curve constructor
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///
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SplineCurve::SplineCurve() {
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type = CURVE_INVALID;
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}
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/// @brief Split a curve in two using the de Casteljau algorithm
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/// @param c1
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/// @param c2
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/// @param t
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///
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void SplineCurve::Split(SplineCurve &c1,SplineCurve &c2,float t) {
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// Split a line
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if (type == CURVE_LINE) {
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c1.type = CURVE_LINE;
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c2.type = CURVE_LINE;
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c1.p1 = p1;
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c2.p2 = p2;
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c1.p2 = p1*(1-t)+p2*t;
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c2.p1 = c1.p2;
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}
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// Split a bicubic
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else if (type == CURVE_BICUBIC) {
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c1.type = CURVE_BICUBIC;
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c2.type = CURVE_BICUBIC;
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// Sub-divisions
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float u = 1-t;
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Vector2D p12 = p1*u+p2*t;
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Vector2D p23 = p2*u+p3*t;
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Vector2D p34 = p3*u+p4*t;
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Vector2D p123 = p12*u+p23*t;
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Vector2D p234 = p23*u+p34*t;
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Vector2D p1234 = p123*u+p234*t;
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// Set points
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c1.p1 = p1;
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c2.p4 = p4;
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c1.p2 = p12;
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c1.p3 = p123;
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c1.p4 = p1234;
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c2.p1 = p1234;
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c2.p2 = p234;
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c2.p3 = p34;
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}
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}
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/// @brief Based on http://antigrain.com/research/bezier_interpolation/index.html Smoothes the curve
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/// @param P0
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/// @param P3
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/// @param smooth
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/// @return
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///
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void SplineCurve::Smooth(Vector2D const& P0,Vector2D const& P3,float smooth) {
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// Validate
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if (type != CURVE_LINE) return;
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if (p1 == p2) return;
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smooth = mid(0.f,smooth,1.f);
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// Get points
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Vector2D P1 = p1;
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Vector2D P2 = p2;
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// Calculate intermediate points
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Vector2D c1 = (P0+P1)/2.f;
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Vector2D c2 = (P1+P2)/2.f;
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Vector2D c3 = (P2+P3)/2.f;
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float len1 = (P1-P0).Len();
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float len2 = (P2-P1).Len();
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float len3 = (P3-P2).Len();
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float k1 = len1/(len1+len2);
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float k2 = len2/(len2+len3);
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Vector2D m1 = c1+(c2-c1)*k1;
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Vector2D m2 = c2+(c3-c2)*k2;
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// Set curve points
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p4 = p2;
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p2 = m1+(c2-m1)*smooth + P1 - m1;
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p3 = m2+(c2-m2)*smooth + P2 - m2;
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type = CURVE_BICUBIC;
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}
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/// @brief Get a point
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/// @param t
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/// @return
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///
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Vector2D SplineCurve::GetPoint(float t) const {
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if (type == CURVE_POINT) return p1;
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if (type == CURVE_LINE) {
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return p1*(1.f-t) + p2*t;
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}
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if (type == CURVE_BICUBIC) {
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float u = 1.f-t;
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return p1*u*u*u + 3*p2*t*u*u + 3*p3*t*t*u + p4*t*t*t;
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}
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return Vector2D(0,0);
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}
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Vector2D& SplineCurve::EndPoint() {
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switch (type) {
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case CURVE_POINT: return p1;
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case CURVE_LINE: return p2;
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case CURVE_BICUBIC: return p4;
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default: return p1;
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}
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}
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/// @brief Get point closest to reference
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/// @param ref
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/// @return
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///
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Vector2D SplineCurve::GetClosestPoint(Vector2D const& ref) const {
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return GetPoint(GetClosestParam(ref));
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}
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/// @brief Get value of parameter closest to point
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/// @param ref
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/// @return
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///
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float SplineCurve::GetClosestParam(Vector2D const& ref) const {
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if (type == CURVE_LINE) {
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return GetClosestSegmentPart(p1,p2,ref);
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}
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if (type == CURVE_BICUBIC) {
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int steps = 100;
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float bestDist = 80000000.f;
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float bestT = 0.f;
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for (int i=0;i<=steps;i++) {
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float t = float(i)/float(steps);
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float dist = (GetPoint(t)-ref).Len();
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if (dist < bestDist) {
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bestDist = dist;
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bestT = t;
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}
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}
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return bestT;
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}
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return 0.f;
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}
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/// @brief Quick distance
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/// @param ref
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/// @return
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///
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float SplineCurve::GetQuickDistance(Vector2D const& ref) const {
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using std::min;
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if (type == CURVE_BICUBIC) {
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float len1 = GetClosestSegmentDistance(p1,p2,ref);
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float len2 = GetClosestSegmentDistance(p2,p3,ref);
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float len3 = GetClosestSegmentDistance(p3,p4,ref);
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float len4 = GetClosestSegmentDistance(p4,p1,ref);
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float len5 = GetClosestSegmentDistance(p1,p3,ref);
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float len6 = GetClosestSegmentDistance(p2,p4,ref);
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return min(min(min(len1,len2),min(len3,len4)),min(len5,len6));
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}
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// Something else
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else return (GetClosestPoint(ref)-ref).Len();
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}
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/// @brief Closest t in segment p1-p2 to point p3
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/// @param pt1
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/// @param pt2
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/// @param pt3
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/// @return
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///
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float SplineCurve::GetClosestSegmentPart(Vector2D const& pt1,Vector2D const& pt2,Vector2D const& pt3) const {
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return mid(0.f,(pt3-pt1).Dot(pt2-pt1)/(pt2-pt1).SquareLen(),1.f);
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}
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/// @brief Closest distance between p3 and segment p1-p2
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/// @param pt1
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/// @param pt2
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/// @param pt3
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///
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float SplineCurve::GetClosestSegmentDistance(Vector2D const& pt1,Vector2D const& pt2,Vector2D const& pt3) const {
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float t = GetClosestSegmentPart(pt1,pt2,pt3);
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return (pt1*(1.f-t)+pt2*t-pt3).Len();
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}
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