7 |
|
|
8 |
|
#include "copyright.h" |
9 |
|
|
10 |
+ |
#define _USE_MATH_DEFINES |
11 |
|
#include <math.h> |
12 |
|
#include "fvect.h" |
13 |
|
|
14 |
+ |
double |
15 |
+ |
Acos(double x) /* insurance for touchy math library */ |
16 |
+ |
{ |
17 |
+ |
if (x <= -1.+FTINY*FTINY) |
18 |
+ |
return(M_PI); |
19 |
+ |
if (x >= 1.-FTINY*FTINY) |
20 |
+ |
return(.0); |
21 |
+ |
return(acos(x)); |
22 |
+ |
} |
23 |
|
|
24 |
|
double |
25 |
+ |
Asin(double x) /* insurance for touchy math library */ |
26 |
+ |
{ |
27 |
+ |
if (x <= -1.+FTINY*FTINY) |
28 |
+ |
return(-M_PI/2.); |
29 |
+ |
if (x >= 1.-FTINY*FTINY) |
30 |
+ |
return(M_PI/2); |
31 |
+ |
return(asin(x)); |
32 |
+ |
} |
33 |
+ |
|
34 |
+ |
double |
35 |
|
fdot( /* return the dot product of two vectors */ |
36 |
< |
register FVECT v1, |
37 |
< |
register FVECT v2 |
36 |
> |
const FVECT v1, |
37 |
> |
const FVECT v2 |
38 |
|
) |
39 |
|
{ |
40 |
|
return(DOT(v1,v2)); |
43 |
|
|
44 |
|
double |
45 |
|
dist2( /* return square of distance between points */ |
46 |
< |
register FVECT p1, |
47 |
< |
register FVECT p2 |
46 |
> |
const FVECT p1, |
47 |
> |
const FVECT p2 |
48 |
|
) |
49 |
|
{ |
50 |
|
FVECT delta; |
51 |
|
|
52 |
< |
delta[0] = p2[0] - p1[0]; |
33 |
< |
delta[1] = p2[1] - p1[1]; |
34 |
< |
delta[2] = p2[2] - p1[2]; |
52 |
> |
VSUB(delta, p2, p1); |
53 |
|
|
54 |
|
return(DOT(delta, delta)); |
55 |
|
} |
57 |
|
|
58 |
|
double |
59 |
|
dist2line( /* return square of distance to line */ |
60 |
< |
FVECT p, /* the point */ |
61 |
< |
FVECT ep1, |
62 |
< |
FVECT ep2 /* points on the line */ |
60 |
> |
const FVECT p, /* the point */ |
61 |
> |
const FVECT ep1, |
62 |
> |
const FVECT ep2 /* points on the line */ |
63 |
|
) |
64 |
|
{ |
65 |
< |
register double d, d1, d2; |
65 |
> |
double d, d1, d2; |
66 |
|
|
67 |
|
d = dist2(ep1, ep2); |
68 |
|
d1 = dist2(ep1, p); |
74 |
|
|
75 |
|
double |
76 |
|
dist2lseg( /* return square of distance to line segment */ |
77 |
< |
FVECT p, /* the point */ |
78 |
< |
FVECT ep1, |
79 |
< |
FVECT ep2 /* the end points */ |
77 |
> |
const FVECT p, /* the point */ |
78 |
> |
const FVECT ep1, |
79 |
> |
const FVECT ep2 /* the end points */ |
80 |
|
) |
81 |
|
{ |
82 |
< |
register double d, d1, d2; |
82 |
> |
double d, d1, d2; |
83 |
|
|
84 |
|
d = dist2(ep1, ep2); |
85 |
|
d1 = dist2(ep1, p); |
100 |
|
|
101 |
|
void |
102 |
|
fcross( /* vres = v1 X v2 */ |
103 |
< |
register FVECT vres, |
104 |
< |
register FVECT v1, |
105 |
< |
register FVECT v2 |
103 |
> |
FVECT vres, |
104 |
> |
const FVECT v1, |
105 |
> |
const FVECT v2 |
106 |
|
) |
107 |
|
{ |
108 |
< |
vres[0] = v1[1]*v2[2] - v1[2]*v2[1]; |
91 |
< |
vres[1] = v1[2]*v2[0] - v1[0]*v2[2]; |
92 |
< |
vres[2] = v1[0]*v2[1] - v1[1]*v2[0]; |
108 |
> |
VCROSS(vres, v1, v2); |
109 |
|
} |
110 |
|
|
111 |
|
|
112 |
|
void |
113 |
|
fvsum( /* vres = v0 + f*v1 */ |
114 |
< |
register FVECT vres, |
115 |
< |
register FVECT v0, |
116 |
< |
register FVECT v1, |
117 |
< |
register double f |
114 |
> |
FVECT vres, |
115 |
> |
const FVECT v0, |
116 |
> |
const FVECT v1, |
117 |
> |
double f |
118 |
|
) |
119 |
|
{ |
120 |
< |
vres[0] = v0[0] + f*v1[0]; |
105 |
< |
vres[1] = v0[1] + f*v1[1]; |
106 |
< |
vres[2] = v0[2] + f*v1[2]; |
120 |
> |
VSUM(vres, v0, v1, f); |
121 |
|
} |
122 |
|
|
123 |
|
|
124 |
|
double |
125 |
|
normalize( /* normalize a vector, return old magnitude */ |
126 |
< |
register FVECT v |
126 |
> |
FVECT v |
127 |
|
) |
128 |
|
{ |
129 |
< |
register double len, d; |
129 |
> |
double len, d; |
130 |
|
|
131 |
|
d = DOT(v, v); |
132 |
|
|
133 |
< |
if (d <= FTINY*FTINY) |
133 |
> |
if (d == 0.0) |
134 |
|
return(0.0); |
135 |
|
|
136 |
< |
if (d <= 1.0+FTINY && d >= 1.0-FTINY) |
136 |
> |
if ((d <= 1.0+FTINY) & (d >= 1.0-FTINY)) { |
137 |
|
len = 0.5 + 0.5*d; /* first order approximation */ |
138 |
< |
else |
138 |
> |
d = 2.0 - len; |
139 |
> |
} else { |
140 |
|
len = sqrt(d); |
141 |
< |
|
142 |
< |
v[0] *= d = 1.0/len; |
141 |
> |
d = 1.0/len; |
142 |
> |
} |
143 |
> |
v[0] *= d; |
144 |
|
v[1] *= d; |
145 |
|
v[2] *= d; |
146 |
|
|
151 |
|
int |
152 |
|
closestapproach( /* closest approach of two rays */ |
153 |
|
RREAL t[2], /* returned distances along each ray */ |
154 |
< |
FVECT rorg0, /* first origin */ |
155 |
< |
FVECT rdir0, /* first direction (normalized) */ |
156 |
< |
FVECT rorg1, /* second origin */ |
157 |
< |
FVECT rdir1 /* second direction (normalized) */ |
154 |
> |
const FVECT rorg0, /* first origin */ |
155 |
> |
const FVECT rdir0, /* first direction (normalized) */ |
156 |
> |
const FVECT rorg1, /* second origin */ |
157 |
> |
const FVECT rdir1 /* second direction (normalized) */ |
158 |
|
) |
159 |
|
{ |
160 |
|
double dotprod = DOT(rdir0, rdir1); |
174 |
|
} |
175 |
|
|
176 |
|
|
161 |
– |
#if 0 |
162 |
– |
int |
163 |
– |
closestapproach( /* closest approach of two rays */ |
164 |
– |
RREAL t[2], /* returned distances along each ray */ |
165 |
– |
FVECT rorg0, /* first origin */ |
166 |
– |
FVECT rdir0, /* first direction (unnormalized) */ |
167 |
– |
FVECT rorg1, /* second origin */ |
168 |
– |
FVECT rdir1 /* second direction (unnormalized) */ |
169 |
– |
) |
170 |
– |
{ |
171 |
– |
double dotprod = DOT(rdir0, rdir1); |
172 |
– |
double d0n2 = DOT(rdir0, rdir0); |
173 |
– |
double d1n2 = DOT(rdir1, rdir1); |
174 |
– |
double denom = d0n2*d1n2 - dotprod*dotprod; |
175 |
– |
double o1o2_d1; |
176 |
– |
FVECT o0o1; |
177 |
– |
|
178 |
– |
if (denom <= FTINY) { /* check if lines are parallel */ |
179 |
– |
t[0] = t[1] = 0.0; |
180 |
– |
return(0); |
181 |
– |
} |
182 |
– |
VSUB(o0o1, rorg0, rorg1); |
183 |
– |
o1o2_d1 = DOT(o0o1, rdir1); |
184 |
– |
t[0] = (o1o2_d1*dotprod - DOT(o0o1,rdir0)*d1n2) / denom; |
185 |
– |
t[1] = (o1o2_d1 + t[0]*dotprod) / d1n2; |
186 |
– |
return(1); |
187 |
– |
} |
188 |
– |
#endif |
189 |
– |
|
190 |
– |
|
177 |
|
void |
178 |
|
spinvector( /* rotate vector around normal */ |
179 |
< |
FVECT vres, /* returned vector */ |
180 |
< |
FVECT vorig, /* original vector */ |
181 |
< |
FVECT vnorm, /* normalized vector for rotation */ |
182 |
< |
double theta /* left-hand radians */ |
179 |
> |
FVECT vres, /* returned vector (same magnitude as vorig) */ |
180 |
> |
const FVECT vorig, /* original vector */ |
181 |
> |
const FVECT vnorm, /* normalized vector for rotation */ |
182 |
> |
double theta /* right-hand radians */ |
183 |
|
) |
184 |
|
{ |
185 |
|
double sint, cost, normprod; |
186 |
|
FVECT vperp; |
187 |
< |
register int i; |
187 |
> |
int i; |
188 |
|
|
189 |
|
if (theta == 0.0) { |
190 |
|
if (vres != vorig) |
194 |
|
cost = cos(theta); |
195 |
|
sint = sin(theta); |
196 |
|
normprod = DOT(vorig, vnorm)*(1.-cost); |
197 |
< |
fcross(vperp, vnorm, vorig); |
197 |
> |
VCROSS(vperp, vnorm, vorig); |
198 |
|
for (i = 0; i < 3; i++) |
199 |
|
vres[i] = vorig[i]*cost + vnorm[i]*normprod + vperp[i]*sint; |
200 |
+ |
} |
201 |
+ |
|
202 |
+ |
double |
203 |
+ |
geodesic( /* rotate vector on great circle towards target */ |
204 |
+ |
FVECT vres, /* returned vector (same magnitude as vorig) */ |
205 |
+ |
const FVECT vorig, /* original vector */ |
206 |
+ |
const FVECT vtarg, /* vector we are rotating towards */ |
207 |
+ |
double t, /* amount along arc directed towards vtarg */ |
208 |
+ |
int meas /* distance measure (radians, absolute, relative) */ |
209 |
+ |
) |
210 |
+ |
{ |
211 |
+ |
FVECT normtarg; |
212 |
+ |
double volen, dotprod, sintr, cost; |
213 |
+ |
int i; |
214 |
+ |
|
215 |
+ |
VCOPY(normtarg, vtarg); /* in case vtarg==vres */ |
216 |
+ |
if (vres != vorig) |
217 |
+ |
VCOPY(vres, vorig); |
218 |
+ |
if (t == 0.0) |
219 |
+ |
return(VLEN(vres)); /* no rotation requested */ |
220 |
+ |
if ((volen = normalize(vres)) == 0.0) |
221 |
+ |
return(0.0); |
222 |
+ |
if (normalize(normtarg) == 0.0) |
223 |
+ |
return(0.0); /* target vector is zero */ |
224 |
+ |
dotprod = DOT(vres, normtarg); |
225 |
+ |
/* check for colinear */ |
226 |
+ |
if (dotprod >= 1.0-FTINY*FTINY) { |
227 |
+ |
if (meas != GEOD_REL) |
228 |
+ |
return(0.0); |
229 |
+ |
vres[0] *= volen; vres[1] *= volen; vres[2] *= volen; |
230 |
+ |
return(volen); |
231 |
+ |
} |
232 |
+ |
if (dotprod <= -1.0+FTINY*FTINY) |
233 |
+ |
return(0.0); |
234 |
+ |
if (meas == GEOD_ABS) |
235 |
+ |
t /= volen; |
236 |
+ |
else if (meas == GEOD_REL) |
237 |
+ |
t *= acos(dotprod); |
238 |
+ |
cost = cos(t); |
239 |
+ |
sintr = sin(t) / sqrt(1. - dotprod*dotprod); |
240 |
+ |
for (i = 0; i < 3; i++) |
241 |
+ |
vres[i] = volen*( cost*vres[i] + |
242 |
+ |
sintr*(normtarg[i] - dotprod*vres[i]) ); |
243 |
+ |
|
244 |
+ |
return(volen); /* return vector length */ |
245 |
|
} |