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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308
|
/*
* Copyright (C) Volition, Inc. 1999. All rights reserved.
*
* All source code herein is the property of Volition, Inc. You may not sell
* or otherwise commercially exploit the source or things you created based on the
* source.
*
*/
#include "globalincs/alphacolors.h"
#include "graphics/2d.h"
#include "math/spline.h"
#include "render/3d.h"
// -------------------------------------------------------------------------------------------------
// SPLINE DEFINES/VARS
//
// -------------------------------------------------------------------------------------------------
// SPLINE FUNCTIONS
//
static float bez_fact_lookup[13] = {
1.0f, // 0!
1.0f, // 1!
2.0f, // 2!
6.0f, // 3!
24.0f, // 4!
120.0f, // 5!
720.0f, // 6!
5040.0f, // 7!
40320.0f, // 8!
362880.0f, // 9!
3628800.0f, // 10!
39916800.0f, // 11!
479001600.0f, // 12!
};
// Limited Factorial
static float bez_fact(int n)
{
Assert((n >= 0) && (n <= 12));
return bez_fact_lookup[n];
}
// bez constructor
bez_spline::bez_spline()
{
int idx;
// zero all points
for(idx=0; idx<MAX_BEZ_PTS; idx++){
pts[idx] = vmd_zero_vector;
}
num_pts = 0;
}
// bez constructor
bez_spline::bez_spline(int _num_pts, vec3d *_pts[MAX_BEZ_PTS])
{
bez_set_points(_num_pts, _pts);
}
// set control points
void bez_spline::bez_set_points(int _num_pts, vec3d *_pts[MAX_BEZ_PTS])
{
int idx;
// store the points
num_pts = _num_pts;
for(idx=0; idx<_num_pts; idx++){
Assert(_pts[idx] != NULL);
if(_pts[idx] != NULL){
pts[idx] = *_pts[idx];
}
}
}
// blend function
#define COMB(_n, _k) (bez_fact(_n) / (bez_fact(_k) * bez_fact(_n - _k)))
float bez_spline::BEZ(int k, int n, float u)
{
float a = (float)COMB(n, k);
float b = (float)pow(u, (float)k);
float c = (float)pow(1.0f - u, (float)(n - k));
return a * b * c;
}
// get a point on the curve
void bez_spline::bez_get_point(vec3d *out, float u)
{
int idx;
float bez_val;
Assert(out != NULL);
if(out == NULL){
return;
}
// calc
out->xyz.x = 0.0f;
out->xyz.y = 0.0f;
out->xyz.z = 0.0f;
for(idx=0; idx<num_pts; idx++){
// bez val
bez_val = BEZ(idx, num_pts-1, u);
// x component
out->xyz.x += pts[idx].xyz.x * bez_val;
// y component
out->xyz.y += pts[idx].xyz.y * bez_val;
// z component
out->xyz.z += pts[idx].xyz.z * bez_val;
}
}
// render a bezier
void bez_spline::bez_render(int divs, color *c)
{
float inc;
int idx;
vertex a, b;
vec3d pt;
// bleh
if(divs <= 0){
return;
}
inc = 1.0f / (float)divs;
// draw in red
gr_set_color_fast(c);
// draw that many divisions
bez_get_point(&pt, 0.0f);
g3_rotate_vertex(&a, &pt);
for(idx=1; idx<=divs; idx++){
// second point
bez_get_point(&pt, (float)idx * inc);
g3_rotate_vertex(&b, &pt);
// draw the line
g3_draw_line(&a, &b);
// store b
a = b;
}
// draw the control points
gr_set_color_fast(&Color_bright_green);
for(idx=0; idx<num_pts; idx++){
g3_draw_sphere_ez(&pts[idx], 0.75f);
}
}
// --------------------------------------------------------------------------
// HERMITE splines
// constructor
herm_spline::herm_spline()
{
int idx;
// zero all points
for(idx=0; idx<MAX_HERM_PTS; idx++){
pts[idx] = vmd_zero_vector;
d_pts[idx] = vmd_zero_vector;
}
num_pts = 0;
}
// constructor
herm_spline::herm_spline(int _num_pts, vec3d *_pts[MAX_HERM_PTS], vec3d *_d_pts[MAX_HERM_PTS])
{
herm_set_points(_num_pts, _pts, _d_pts);
}
// set the points
void herm_spline::herm_set_points(int _num_pts, vec3d *_pts[MAX_HERM_PTS], vec3d *_d_pts[MAX_HERM_PTS])
{
int idx;
// store the points
num_pts = _num_pts;
for(idx=0; idx<_num_pts; idx++){
Assert(_pts[idx] != NULL);
if(_pts[idx] != NULL){
pts[idx] = *_pts[idx];
}
Assert(_d_pts[idx] != NULL);
if(_d_pts[idx] != NULL){
d_pts[idx] = *_d_pts[idx];
}
}
}
// get a point on the hermite curve.
void herm_spline::herm_get_point(vec3d *out, float u, int k)
{
float a = ( (2.0f * u * u * u) - (3.0f * u * u) + 1 );
float b = ( (-2.0f * u * u * u) + (3.0f * u * u) );
float c = ( (u * u * u) - (2.0f * u * u) + u );
float d = ( (u * u * u) - (u * u) );
vec3d va;
vm_vec_copy_scale(&va, &pts[k], a);
vec3d vb;
vm_vec_copy_scale(&vb, &pts[k+1], b);
vec3d vc;
vm_vec_copy_scale(&vc, &d_pts[k], c);
vec3d vd;
vm_vec_copy_scale(&vd, &d_pts[k+1], d);
vm_vec_add(out, &va, &vb);
vm_vec_add2(out, &vc);
vm_vec_add2(out, &vd);
}
// the derivative of a point on the hermite curve
void herm_spline::herm_get_deriv(vec3d *deriv, float u, int k)
{
float a = ( (6.0f * u * u) - (6.0f * u) );
float b = ( (-6.0f * u * u) + (6.0f * u) );
float c = ( (3.0f * u * u) - (4.0f * u) + 1 );
float d = ( (3.0f * u * u) - (2.0f * u) );
vec3d va;
vm_vec_copy_scale(&va, &pts[k], a);
vec3d vb;
vm_vec_copy_scale(&vb, &pts[k+1], b);
vec3d vc;
vm_vec_copy_scale(&vc, &d_pts[k], c);
vec3d vd;
vm_vec_copy_scale(&vd, &d_pts[k+1], d);
vm_vec_add(deriv, &va, &vb);
vm_vec_add2(deriv, &vc);
vm_vec_add2(deriv, &vd);
}
// render a bezier
void herm_spline::herm_render(int divs, color *clc)
{
int idx;
int s_idx;
float inc = 1.0f / (float)divs;
vertex a, b, c;
vec3d pt, d_pt;
// draw in red
gr_set_color_fast(clc);
// render each section
for(idx=0; idx<num_pts-1; idx++){
// render this piece
herm_get_point(&pt, 0.0f, idx);
g3_rotate_vertex(&a, &pt);
// draw the deriv
herm_get_deriv(&d_pt, 0.0f, idx);
vm_vec_add2(&d_pt, &pt);
g3_rotate_vertex(&c, &d_pt);
g3_draw_line(&a, &c);
for(s_idx=1; s_idx<divs * 2; s_idx++){
// second point
herm_get_point(&pt, (float)s_idx * inc, idx);
// 2nd point on the line
g3_rotate_vertex(&b, &pt);
// draw the line
g3_draw_line(&a, &b);
// draw the deriv line
herm_get_deriv(&d_pt, (float)s_idx * inc, idx);
vm_vec_add2(&d_pt, &pt);
g3_rotate_vertex(&c, &d_pt);
g3_draw_line(&b, &c);
// store b
a = b;
}
}
// draw the control points
gr_set_color_fast(&Color_bright_green);
for(idx=0; idx<num_pts; idx++){
g3_draw_sphere_ez(&pts[idx], 0.75f);
}
}
|