/usr/include/rheolef/cad-bezier.h is in librheolef-dev 5.93-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 | #ifndef _RHEO_CAD_BEZIER_H
#define _RHEO_CAD_BEZIER_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
#include "rheolef/cad_element.h"
namespace rheolef {
//
// Evaluate a Bezier curve/surface using Horner algorithm.
//
// from qmg-2.0.2/src/common/qpatchmath.cpp: get_real_point()
//
// see also :
// J.-J. Risler
// Methodes mathematiques pour la CAO
// Masson, coll. RMA, vol. 18, 1991
//
// Evaluate a one-variable Bezier curve using Horner algorithm.
template<class PointArray, class Patch, class T, class Size>
T
eval_bezier_edge (
const T& param,
const Patch& cp_idx, // control point indexes,
Size degree,
Size k, // active coord index in 0...phys_dim-1
const PointArray& x)
{
T u = 1.0 - param;
T pwrv = 1.0;
T result = 0.0;
Size binom = 1;
for (Size j = 0; j < degree + 1; ++j) {
result *= u;
result += T(binom) * pwrv * x[cp_idx[j]][k];
pwrv *= param;
binom *= (degree - j);
binom /= (j + 1);
}
return result;
}
// Compute real coord from param coord using Horner's algorithm.
template<class PointArray, class Patch, class T, class Size>
T
eval_bezier_triangle (
const T& param0,
const T& param1,
const Patch& cp_idx, // control point indexes,
Size degree,
Size k,
const PointArray& x)
{
T p0 = param0;
T p1 = param1;
T p2 = 1.0 - p0 - p1;
Size outer_binom = 1;
T pwrv = 1.0;
T result = 0.0;
for (Size row = degree; row >= 0; --row) {
Size base_idx = row * (row + 1) / 2;
Size inner_binom = 1;
T pwru = 1.0;
T row_result = 0.0;
for (Size col = 0; col <= row; ++col) {
row_result *= p2;
row_result += T(inner_binom) * x[cp_idx[base_idx + col]][k] * pwru;
pwru *= p0;
inner_binom *= (row - col);
inner_binom /= (col + 1);
}
result += row_result * pwrv * T(outer_binom);
outer_binom *= row;
outer_binom /= (degree - row + 1);
pwrv *= p1;
}
return result;
}
// Horner algorithm for evaluating bezier quad (parametric
// to real conversion)
template<class PointArray, class Patch, class T, class Size>
T
eval_bezier_quadrangle (
const T& param0,
const T& param1,
const Patch& cp_idx, // control point indexes,
Size degree1,
Size degree2,
Size k,
const PointArray& x)
{
T u = param0;
T oppu = 1.0 - u;
T v = param1;
T oppv = 1.0 - v;
Size outer_binom = 1;
T outer_result = 0.0;
T pwrv = 1.0;
for (Size d2 = 0; d2 <= degree2; ++d2) {
// Compute the inner coefficient.
Size inner_binom = 1;
T pwru = 1.0;
T inner_result = 0.0;
for (Size d1 = 0; d1 <= degree1; ++d1) {
inner_result *= oppu;
inner_result += x[cp_idx[d2 * (degree1 + 1) + d1]][k] * T(inner_binom) * pwru;
pwru *= u;
inner_binom *= (degree1 - d1);
inner_binom /= (d1 + 1);
}
outer_result *= oppv;
outer_result += inner_result * T(outer_binom) * pwrv;
pwrv *= v;
outer_binom *= (degree2 - d2);
outer_binom /= (d2 + 1);
}
return outer_result;
}
}// namespace rheolef
#endif // _RHEO_CAD_BEZIER_H
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