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arith3 4.3 KB

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