forked from enlightenment/efl
331 lines
9.3 KiB
C
331 lines
9.3 KiB
C
/* EINA - EFL data type library
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* Copyright (C) 2015 Subhransu Mohanty
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library;
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* if not, see <http://www.gnu.org/licenses/>.
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*/
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#include <math.h>
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#include <float.h>
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#include <stdio.h>
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#include "eina_private.h"
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#include "eina_bezier.h"
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#include "eina_util.h"
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static void
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_eina_bezier_1st_derivative(const Eina_Bezier *bz,
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double t,
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double *px, double *py)
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{
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// p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3)
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double m_t = 1. - t;
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double d = t * t;
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double a = -m_t * m_t;
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double b = 1 - 4 * t + 3 * d;
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double c = 2 * t - 3 * d;
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*px = 3 * ( a * bz->start.x + b * bz->ctrl_start.x + c * bz->ctrl_end.x + d * bz->end.x);
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*py = 3 * ( a * bz->start.y + b * bz->ctrl_start.y + c * bz->ctrl_end.y + d * bz->end.y);
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}
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// Approximate sqrt(x*x + y*y) using the alpha max plus beta min algorithm.
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// This uses alpha = 1, beta = 3/8, which results in a maximum error of less
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// than 7% compared to the correct value.
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static double
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_line_length(double x1, double y1, double x2, double y2)
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{
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double x = x2 - x1;
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double y = y2 - y1;
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x = x < 0 ? -x : x;
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y = y < 0 ? -y : y;
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return (x > y ? x + 0.375 * y : y + 0.375 * x);
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}
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static void
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_eina_bezier_split(const Eina_Bezier *b,
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Eina_Bezier *first, Eina_Bezier *second)
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{
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double c = (b->ctrl_start.x + b->ctrl_end.x) * 0.5;
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first->ctrl_start.x = (b->start.x + b->ctrl_start.x) * 0.5;
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second->ctrl_end.x = (b->ctrl_end.x + b->end.x) * 0.5;
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first->start.x = b->start.x;
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second->end.x = b->end.x;
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first->ctrl_end.x = (first->ctrl_start.x + c) * 0.5;
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second->ctrl_start.x = (second->ctrl_end.x + c) * 0.5;
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first->end.x = second->start.x = (first->ctrl_end.x + second->ctrl_start.x) * 0.5;
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c = (b->ctrl_start.y + b->ctrl_end.y) / 2;
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first->ctrl_start.y = (b->start.y + b->ctrl_start.y) * 0.5;
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second->ctrl_end.y = (b->ctrl_end.y + b->end.y) * 0.5;
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first->start.y = b->start.y;
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second->end.y = b->end.y;
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first->ctrl_end.y = (first->ctrl_start.y + c) * 0.5;
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second->ctrl_start.y = (second->ctrl_end.y + c) * 0.5;
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first->end.y = second->start.y = (first->ctrl_end.y + second->ctrl_start.y) * 0.5;
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}
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static float
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_eina_bezier_length_helper(const Eina_Bezier *b)
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{
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Eina_Bezier left, right; /* bez poly splits */
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float len = 0.0; /* arc length */
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float chord; /* chord length */
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float length;
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len = len + _line_length(b->start.x, b->start.y, b->ctrl_start.x, b->ctrl_start.y);
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len = len + _line_length(b->ctrl_start.x, b->ctrl_start.y, b->ctrl_end.x, b->ctrl_end.y);
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len = len + _line_length(b->ctrl_end.x, b->ctrl_end.y, b->end.x, b->end.y);
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chord = _line_length(b->start.x, b->start.y, b->end.x, b->end.y);
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if (!EINA_FLT_EQ(len, chord)) {
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_eina_bezier_split(b, &left, &right); /* split in two */
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length =
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_eina_bezier_length_helper(&left) + /* try left side */
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_eina_bezier_length_helper(&right); /* try right side */
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return length;
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}
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return len;
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}
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EAPI void
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eina_bezier_values_set(Eina_Bezier *b,
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double start_x, double start_y,
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double ctrl_start_x, double ctrl_start_y,
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double ctrl_end_x, double ctrl_end_y,
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double end_x, double end_y)
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{
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b->start.x = start_x;
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b->start.y = start_y;
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b->ctrl_start.x = ctrl_start_x;
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b->ctrl_start.y = ctrl_start_y;
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b->ctrl_end.x = ctrl_end_x;
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b->ctrl_end.y = ctrl_end_y;
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b->end.x = end_x;
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b->end.y = end_y;
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}
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EAPI void
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eina_bezier_values_get(const Eina_Bezier *b,
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double *start_x, double *start_y,
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double *ctrl_start_x, double *ctrl_start_y,
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double *ctrl_end_x, double *ctrl_end_y,
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double *end_x, double *end_y)
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{
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if (start_x) *start_x = b->start.x;
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if (start_y) *start_y = b->start.y;
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if (ctrl_start_x) *ctrl_start_x = b->ctrl_start.x;
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if (ctrl_start_y) *ctrl_start_y = b->ctrl_start.y;
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if (ctrl_end_x) *ctrl_end_x = b->ctrl_end.x;
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if (ctrl_end_y) *ctrl_end_y = b->ctrl_end.y;
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if (end_x) *end_x = b->end.x;
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if (end_y) *end_y = b->end.y;
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}
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EAPI void
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eina_bezier_point_at(const Eina_Bezier *bz, double t, double *px, double *py)
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{
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double m_t = 1.0 - t;
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if (px)
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{
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double a = bz->start.x * m_t + bz->ctrl_start.x * t;
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double b = bz->ctrl_start.x * m_t + bz->ctrl_end.x * t;
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double c = bz->ctrl_end.x * m_t + bz->end.x * t;
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a = a * m_t + b * t;
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b = b * m_t + c * t;
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*px = a * m_t + b * t;
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}
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if (py)
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{
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double a = bz->start.y * m_t + bz->ctrl_start.y * t;
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double b = bz->ctrl_start.y * m_t + bz->ctrl_end.y * t;
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double c = bz->ctrl_end.y * m_t + bz->end.y * t;
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a = a * m_t + b * t;
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b = b * m_t + c * t;
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*py = a * m_t + b * t;
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}
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}
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EAPI double
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eina_bezier_angle_at(const Eina_Bezier *b, double t)
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{
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double x, y;
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double theta;
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double theta_normalized;
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_eina_bezier_1st_derivative(b, t, &x, &y);
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theta = atan2(y, x) * 360.0 / (M_PI * 2);
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theta_normalized = theta < 0 ? theta + 360 : theta;
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return theta_normalized;
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}
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EAPI double
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eina_bezier_length_get(const Eina_Bezier *b)
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{
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return _eina_bezier_length_helper(b);
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}
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static void
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_eina_bezier_split_left(Eina_Bezier *b, double t, Eina_Bezier *left)
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{
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Eina_Bezier local;
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if (!left) left = &local;
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left->start.x = b->start.x;
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left->start.y = b->start.y;
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left->ctrl_start.x = b->start.x + t * ( b->ctrl_start.x - b->start.x );
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left->ctrl_start.y = b->start.y + t * ( b->ctrl_start.y - b->start.y );
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left->ctrl_end.x = b->ctrl_start.x + t * ( b->ctrl_end.x - b->ctrl_start.x ); // temporary holding spot
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left->ctrl_end.y = b->ctrl_start.y + t * ( b->ctrl_end.y - b->ctrl_start.y ); // temporary holding spot
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b->ctrl_end.x = b->ctrl_end.x + t * ( b->end.x - b->ctrl_end.x );
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b->ctrl_end.y = b->ctrl_end.y + t * ( b->end.y - b->ctrl_end.y );
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b->ctrl_start.x = left->ctrl_end.x + t * ( b->ctrl_end.x - left->ctrl_end.x);
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b->ctrl_start.y = left->ctrl_end.y + t * ( b->ctrl_end.y - left->ctrl_end.y);
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left->ctrl_end.x = left->ctrl_start.x + t * ( left->ctrl_end.x - left->ctrl_start.x );
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left->ctrl_end.y = left->ctrl_start.y + t * ( left->ctrl_end.y - left->ctrl_start.y );
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left->end.x = b->start.x = left->ctrl_end.x + t * (b->ctrl_start.x - left->ctrl_end.x);
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left->end.y = b->start.y = left->ctrl_end.y + t * (b->ctrl_start.y - left->ctrl_end.y);
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}
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EAPI double
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eina_bezier_t_at(const Eina_Bezier *b, double l)
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{
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double len = eina_bezier_length_get(b);
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double biggest = 1.0;
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double t = 1.0;
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if (l >= len)// || (EINA_DBL_EQ(len, l)))
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return t;
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t *= 0.5;
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while (1)
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{
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Eina_Bezier right = *b;
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Eina_Bezier left;
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double ll;
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_eina_bezier_split_left(&right, t, &left);
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ll = eina_bezier_length_get(&left);
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if (EINA_DBL_EQ(ll, l))
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break;
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if (ll < l)
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{
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t += (biggest - t) * 0.5;
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}
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else
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{
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biggest = t;
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t -= t * 0.5;
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}
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}
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return t;
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}
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EAPI void
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eina_bezier_split_at_length(const Eina_Bezier *b, double len,
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Eina_Bezier *left, Eina_Bezier *right)
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{
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Eina_Bezier local;
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double t;
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if (!right) right = &local;
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*right = *b;
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t = eina_bezier_t_at(right, len);
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_eina_bezier_split_left(right, t, left);
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}
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EAPI void
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eina_bezier_bounds_get(const Eina_Bezier *b, double *x, double *y, double *w, double *h)
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{
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double xmin = b->start.x;
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double xmax = b->start.x;
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double ymin = b->start.y;
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double ymax = b->start.y;
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if (b->ctrl_start.x < xmin)
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xmin = b->ctrl_start.x;
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else if (b->ctrl_start.x > xmax)
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xmax = b->ctrl_start.x;
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if (b->ctrl_end.x < xmin)
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xmin = b->ctrl_end.x;
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else if (b->ctrl_end.x > xmax)
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xmax = b->ctrl_end.x;
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if (b->end.x < xmin)
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xmin = b->end.x;
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else if (b->end.x > xmax)
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xmax = b->end.x;
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if (b->ctrl_start.y < ymin)
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ymin = b->ctrl_start.y;
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else if (b->ctrl_start.y > ymax)
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ymax = b->ctrl_start.y;
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if (b->ctrl_end.y < ymin)
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ymin = b->ctrl_end.y;
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else if (b->ctrl_end.y > ymax)
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ymax = b->ctrl_end.y;
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if (b->end.y < ymin)
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ymin = b->end.y;
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else if (b->end.y > ymax)
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ymax = b->end.y;
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if (x) *x = xmin;
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if (y) *y = ymin;
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if (w) *w = xmax - xmin;
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if (h) *h = ymax - ymin;
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}
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EAPI void
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eina_bezier_on_interval(Eina_Bezier *b, double t0, double t1, Eina_Bezier *result)
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{
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Eina_Bezier bezier;
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double t;
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if (EINA_DBL_EQ(t0, 0.0) &&
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EINA_DBL_EQ(t1, 1.0))
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{
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*result = *b;
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return;
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}
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bezier = *b;
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_eina_bezier_split_left(&bezier, t0, result);
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t = (t1-t0)/(1-t0);
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_eina_bezier_split_left(&bezier, t, result);
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}
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