arith3.3 (4396B)
1 .TH ARITH3 3 2 .SH NAME 3 add3, sub3, neg3, div3, mul3, eqpt3, closept3, dot3, cross3, len3, dist3, unit3, midpt3, lerp3, reflect3, nearseg3, pldist3, vdiv3, vrem3, pn2f3, ppp2f3, fff2p3, pdiv4, add4, sub4 \- operations on 3-d points and planes 4 .SH SYNOPSIS 5 .PP 6 .B 7 #include <draw.h> 8 .PP 9 .B 10 #include <geometry.h> 11 .PP 12 .B 13 Point3 add3(Point3 a, Point3 b) 14 .PP 15 .B 16 Point3 sub3(Point3 a, Point3 b) 17 .PP 18 .B 19 Point3 neg3(Point3 a) 20 .PP 21 .B 22 Point3 div3(Point3 a, double b) 23 .PP 24 .B 25 Point3 mul3(Point3 a, double b) 26 .PP 27 .B 28 int eqpt3(Point3 p, Point3 q) 29 .PP 30 .B 31 int closept3(Point3 p, Point3 q, double eps) 32 .PP 33 .B 34 double dot3(Point3 p, Point3 q) 35 .PP 36 .B 37 Point3 cross3(Point3 p, Point3 q) 38 .PP 39 .B 40 double len3(Point3 p) 41 .PP 42 .B 43 double dist3(Point3 p, Point3 q) 44 .PP 45 .B 46 Point3 unit3(Point3 p) 47 .PP 48 .B 49 Point3 midpt3(Point3 p, Point3 q) 50 .PP 51 .B 52 Point3 lerp3(Point3 p, Point3 q, double alpha) 53 .PP 54 .B 55 Point3 reflect3(Point3 p, Point3 p0, Point3 p1) 56 .PP 57 .B 58 Point3 nearseg3(Point3 p0, Point3 p1, Point3 testp) 59 .PP 60 .B 61 double pldist3(Point3 p, Point3 p0, Point3 p1) 62 .PP 63 .B 64 double vdiv3(Point3 a, Point3 b) 65 .PP 66 .B 67 Point3 vrem3(Point3 a, Point3 b) 68 .PP 69 .B 70 Point3 pn2f3(Point3 p, Point3 n) 71 .PP 72 .B 73 Point3 ppp2f3(Point3 p0, Point3 p1, Point3 p2) 74 .PP 75 .B 76 Point3 fff2p3(Point3 f0, Point3 f1, Point3 f2) 77 .PP 78 .B 79 Point3 pdiv4(Point3 a) 80 .PP 81 .B 82 Point3 add4(Point3 a, Point3 b) 83 .PP 84 .B 85 Point3 sub4(Point3 a, Point3 b) 86 .SH DESCRIPTION 87 These routines do arithmetic on points and planes in affine or projective 3-space. 88 Type 89 .B Point3 90 is 91 .IP 92 .EX 93 .ta 6n 94 typedef struct Point3 Point3; 95 struct Point3{ 96 double x, y, z, w; 97 }; 98 .EE 99 .PP 100 Routines whose names end in 101 .B 3 102 operate on vectors or ordinary points in affine 3-space, represented by their Euclidean 103 .B (x,y,z) 104 coordinates. 105 (They assume 106 .B w=1 107 in their arguments, and set 108 .B w=1 109 in their results.) 110 .TF reflect3 111 .TP 112 Name 113 Description 114 .TP 115 .B add3 116 Add the coordinates of two points. 117 .TP 118 .B sub3 119 Subtract coordinates of two points. 120 .TP 121 .B neg3 122 Negate the coordinates of a point. 123 .TP 124 .B mul3 125 Multiply coordinates by a scalar. 126 .TP 127 .B div3 128 Divide coordinates by a scalar. 129 .TP 130 .B eqpt3 131 Test two points for exact equality. 132 .TP 133 .B closept3 134 Is the distance between two points smaller than 135 .IR eps ? 136 .TP 137 .B dot3 138 Dot product. 139 .TP 140 .B cross3 141 Cross product. 142 .TP 143 .B len3 144 Distance to the origin. 145 .TP 146 .B dist3 147 Distance between two points. 148 .TP 149 .B unit3 150 A unit vector parallel to 151 .IR p . 152 .TP 153 .B midpt3 154 The midpoint of line segment 155 .IR pq . 156 .TP 157 .B lerp3 158 Linear interpolation between 159 .I p 160 and 161 .IR q . 162 .TP 163 .B reflect3 164 The reflection of point 165 .I p 166 in the segment joining 167 .I p0 168 and 169 .IR p1 . 170 .TP 171 .B nearseg3 172 The closest point to 173 .I testp 174 on segment 175 .IR "p0 p1" . 176 .TP 177 .B pldist3 178 The distance from 179 .I p 180 to segment 181 .IR "p0 p1" . 182 .TP 183 .B vdiv3 184 Vector divide \(em the length of the component of 185 .I a 186 parallel to 187 .IR b , 188 in units of the length of 189 .IR b . 190 .TP 191 .B vrem3 192 Vector remainder \(em the component of 193 .I a 194 perpendicular to 195 .IR b . 196 Ignoring roundoff, we have 197 .BR "eqpt3(add3(mul3(b, vdiv3(a, b)), vrem3(a, b)), a)" . 198 .PD 199 .PP 200 The following routines convert amongst various representations of points 201 and planes. Planes are represented identically to points, by duality; 202 a point 203 .B p 204 is on a plane 205 .B q 206 whenever 207 .BR p.x*q.x+p.y*q.y+p.z*q.z+p.w*q.w=0 . 208 Although when dealing with affine points we assume 209 .BR p.w=1 , 210 we can't make the same assumption for planes. 211 The names of these routines are extra-cryptic. They contain an 212 .B f 213 (for `face') to indicate a plane, 214 .B p 215 for a point and 216 .B n 217 for a normal vector. 218 The number 219 .B 2 220 abbreviates the word `to.' 221 The number 222 .B 3 223 reminds us, as before, that we're dealing with affine points. 224 Thus 225 .B pn2f3 226 takes a point and a normal vector and returns the corresponding plane. 227 .TF reflect3 228 .TP 229 Name 230 Description 231 .TP 232 .B pn2f3 233 Compute the plane passing through 234 .I p 235 with normal 236 .IR n . 237 .TP 238 .B ppp2f3 239 Compute the plane passing through three points. 240 .TP 241 .B fff2p3 242 Compute the intersection point of three planes. 243 .PD 244 .PP 245 The names of the following routines end in 246 .B 4 247 because they operate on points in projective 4-space, 248 represented by their homogeneous coordinates. 249 .TP 250 pdiv4 251 Perspective division. Divide 252 .B p.w 253 into 254 .IR p 's 255 coordinates, converting to affine coordinates. 256 If 257 .B p.w 258 is zero, the result is the same as the argument. 259 .TP 260 add4 261 Add the coordinates of two points. 262 .PD 263 .TP 264 sub4 265 Subtract the coordinates of two points. 266 .SH SOURCE 267 .B \*9/src/libgeometry 268 .SH "SEE ALSO 269 .MR matrix (3)