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
|
#include "d2.h"
/* One would think that we would include d2-sbasis.h, however,
* you cannot actually include it in anything - only d2 may import it.
* This is due to the trickinesses of template submatching. */
namespace Geom {
SBasis L2(D2<SBasis> const & a, unsigned k) { return sqrt(dot(a, a), k); }
D2<SBasis> multiply(Linear const & a, D2<SBasis> const & b) {
return D2<SBasis>(multiply(a, b[X]), multiply(a, b[Y]));
}
D2<SBasis> multiply(SBasis const & a, D2<SBasis> const & b) {
return D2<SBasis>(multiply(a, b[X]), multiply(a, b[Y]));
}
D2<SBasis> truncate(D2<SBasis> const & a, unsigned terms) {
return D2<SBasis>(truncate(a[X], terms), truncate(a[Y], terms));
}
unsigned sbasis_size(D2<SBasis> const & a) {
return std::max((unsigned) a[0].size(), (unsigned) a[1].size());
}
//TODO: Is this sensical? shouldn't it be like pythagorean or something?
double tail_error(D2<SBasis> const & a, unsigned tail) {
return std::max(a[0].tailError(tail), a[1].tailError(tail));
}
Piecewise<D2<SBasis> > sectionize(D2<Piecewise<SBasis> > const &a) {
Piecewise<SBasis> x = partition(a[0], a[1].cuts), y = partition(a[1], a[0].cuts);
assert(x.size() == y.size());
Piecewise<D2<SBasis> > ret;
for(unsigned i = 0; i < x.size(); i++)
ret.push_seg(D2<SBasis>(x[i], y[i]));
ret.cuts.insert(ret.cuts.end(), x.cuts.begin(), x.cuts.end());
return ret;
}
D2<Piecewise<SBasis> > make_cuts_independant(Piecewise<D2<SBasis> > const &a) {
D2<Piecewise<SBasis> > ret;
for(unsigned d = 0; d < 2; d++) {
for(unsigned i = 0; i < a.size(); i++)
ret[d].push_seg(a[i][d]);
ret[d].cuts.insert(ret[d].cuts.end(), a.cuts.begin(), a.cuts.end());
}
return ret;
}
Piecewise<D2<SBasis> > rot90(Piecewise<D2<SBasis> > const &M){
Piecewise<D2<SBasis> > result;
if (M.empty()) return M;
result.push_cut(M.cuts[0]);
for (unsigned i=0; i<M.size(); i++){
result.push(rot90(M[i]),M.cuts[i+1]);
}
return result;
}
Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a,
Piecewise<D2<SBasis> > const &b){
Piecewise<SBasis > result;
if (a.empty() || b.empty()) return result;
Piecewise<D2<SBasis> > aa = partition(a,b.cuts);
Piecewise<D2<SBasis> > bb = partition(b,a.cuts);
result.push_cut(aa.cuts.front());
for (unsigned i=0; i<aa.size(); i++){
result.push(dot(aa.segs[i],bb.segs[i]),aa.cuts[i+1]);
}
return result;
}
Piecewise<SBasis> cross(Piecewise<D2<SBasis> > const &a,
Piecewise<D2<SBasis> > const &b){
Piecewise<SBasis > result;
if (a.empty() || b.empty()) return result;
Piecewise<D2<SBasis> > aa = partition(a,b.cuts);
Piecewise<D2<SBasis> > bb = partition(b,a.cuts);
result.push_cut(aa.cuts.front());
for (unsigned i=0; i<a.size(); i++){
result.push(cross(aa.segs[i],bb.segs[i]),aa.cuts[i+1]);
}
return result;
}
Piecewise<D2<SBasis> > operator*(Piecewise<D2<SBasis> > const &a, Matrix const &m) {
Piecewise<D2<SBasis> > result;
if(a.empty()) return result;
result.push_cut(a.cuts[0]);
for (unsigned i = 0; i < a.size(); i++) {
result.push(a[i] * m, a.cuts[i+1]);
}
return result;
}
//if tol>0, only force continuity where the jump is smaller than tol.
Piecewise<D2<SBasis> > force_continuity(Piecewise<D2<SBasis> > const &f,
double tol,
bool closed){
if (f.size()==0) return f;
Piecewise<D2<SBasis> > result=f;
unsigned cur = (closed)? 0:1;
unsigned prev = (closed)? f.size()-1:0;
while(cur<f.size()){
Point pt0 = f.segs[prev].at1();
Point pt1 = f.segs[cur ].at0();
if (tol<=0 || L2sq(pt0-pt1)<tol*tol){
pt0 = (pt0+pt1)/2;
for (unsigned dim=0; dim<2; dim++){
SBasis &prev_sb=result.segs[prev][dim];
SBasis &cur_sb =result.segs[cur][dim];
Coord const c=pt0[dim];
if (prev_sb.empty()) {
prev_sb.push_back(Linear(0.0, c));
} else {
prev_sb[0][1] = c;
}
if (cur_sb.empty()) {
cur_sb.push_back(Linear(c, 0.0));
} else {
cur_sb[0][0] = c;
}
}
}
prev = cur++;
}
return result;
}
}
|
