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
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
|
/*
* Copyright (C) 1998, 2000-2007, 2010, 2011, 2012, 2013 SINTEF ICT,
* Applied Mathematics, Norway.
*
* Contact information: E-mail: tor.dokken@sintef.no
* SINTEF ICT, Department of Applied Mathematics,
* P.O. Box 124 Blindern,
* 0314 Oslo, Norway.
*
* This file is part of SISL.
*
* SISL is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as
* published by the Free Software Foundation, either version 3 of the
* License, or (at your option) any later version.
*
* SISL 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 Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public
* License along with SISL. If not, see
* <http://www.gnu.org/licenses/>.
*
* In accordance with Section 7(b) of the GNU Affero General Public
* License, a covered work must retain the producer line in every data
* file that is created or manipulated using SISL.
*
* Other Usage
* You can be released from the requirements of the license by purchasing
* a commercial license. Buying such a license is mandatory as soon as you
* develop commercial activities involving the SISL library without
* disclosing the source code of your own applications.
*
* This file may be used in accordance with the terms contained in a
* written agreement between you and SINTEF ICT.
*/
#include "sisl-copyright.h"
/*
*
* $Id: s6castelja.c,v 1.2 2001-03-19 15:59:00 afr Exp $
*
*/
#define S6DECASTELJAU
#include "sislP.h"
#if defined(SISLNEEDPROTOTYPES)
void
s6deCasteljau(double C[], double a, double b, double t, int k, double D[],
int* jstat)
#else
void s6deCasteljau(C,a,b,t,k,D,jstat)
double C[];
double a,b,t;
int k;
double D[];
int* jstat;
#endif
/*
***************************************************************************
*
*********************************************************************
*
* PURPOSE : To subdivide a 1-dim Bezier curve 'f' at a point 't'
* using the deCasteljau lgorithm, and to calculate
* the value f(t).
*
*
*
*
* INPUT : C[0:k-1] - Bezier coefficients of f relative to the
* intervall [a,b].
* a - start of parameter intervall.
* b - end of parameter intervall.
* t - parameter value at which to subdivide.
* Assumes: a < b , and a <= t <= b.
* k - polynomial order (=degree+1) of f.
* D[0:2*k-1] - allocated space.
*
*
* OUTPUT : D[] - Bezier coefficients for the subdivided repr of 'f'.
* D[r], r=0,...,k-1 - coeffs. on [a,t],
* D[k+r], r=0,...,k-1 - coeffs. on [t,b],
* D[k-1] = D[k] - value of f at t.
*
* METHOD : - The multiaffine blossom F of f at argument
* bags consisting of multipla of a,c, and t are
* calculated using the deCasteljau algorithm. These
* values are stored in an local array A[0:k*k-1]
* as follows:
* A[k*r+j] = F(a,..,a,t,..,t,b,..,b)
* where a is repeated k-1-j times,
* t is repeated r times,
* b is repeated j-r times.
* In particular
* A[k*r+r] r=0,...,k-1 are Bezier coeffs. on [a,t],
* A[k*(k-1-r)+k-1] r=0,...,k-1 : coeffs. on [t,b],
* A[k*(k-1)+k-1] : value of f at t.
*
* jstat - status messages
* < 0 - error
*
*
* REFERENCES :
*
*-
* CALLS :
*
* WRITTEN BY : Kyrre Strom, SI, 93-01.
*
*
****************************************************************************
*/
{
int r,j,kk=k*k,kr;
double alpha;
double Al[16];
double* A = SISL_NULL;
*jstat = 1;
if (a > b || DEQUAL(a,b) ) goto err109;
if (k > 4 )
{
A = newarray(kk,double);
if (A == SISL_NULL) goto err101;
}
else
A = Al;
for (j=0; j<k; j++)
A[j] = C[j];
alpha = (b-t)/(b-a);
for (r = 1; r < k; r++)
for (j = r; j < k; j++)
A[k*r+j] = alpha*A[k*(r-1)+j-1] + (1-alpha)*A[k*(r-1)+j];
for (kk--,kr=r=0; r<k; r++,kr+=k)
{
D[r] = A[kr+r];
D[k+r] = A[kk-kr];
}
goto out;
err109: *jstat = -109;
goto out;
err101: *jstat = -101;
goto out;
out:
if (A != SISL_NULL && A != Al)
freearray(A);
return ;
}
|
