| .TH ARITH3 3 |
| .SH NAME |
| 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 |
| .SH SYNOPSIS |
| .PP |
| .B |
| #include <draw.h> |
| .PP |
| .B |
| #include <geometry.h> |
| .PP |
| .B |
| Point3 add3(Point3 a, Point3 b) |
| .PP |
| .B |
| Point3 sub3(Point3 a, Point3 b) |
| .PP |
| .B |
| Point3 neg3(Point3 a) |
| .PP |
| .B |
| Point3 div3(Point3 a, double b) |
| .PP |
| .B |
| Point3 mul3(Point3 a, double b) |
| .PP |
| .B |
| int eqpt3(Point3 p, Point3 q) |
| .PP |
| .B |
| int closept3(Point3 p, Point3 q, double eps) |
| .PP |
| .B |
| double dot3(Point3 p, Point3 q) |
| .PP |
| .B |
| Point3 cross3(Point3 p, Point3 q) |
| .PP |
| .B |
| double len3(Point3 p) |
| .PP |
| .B |
| double dist3(Point3 p, Point3 q) |
| .PP |
| .B |
| Point3 unit3(Point3 p) |
| .PP |
| .B |
| Point3 midpt3(Point3 p, Point3 q) |
| .PP |
| .B |
| Point3 lerp3(Point3 p, Point3 q, double alpha) |
| .PP |
| .B |
| Point3 reflect3(Point3 p, Point3 p0, Point3 p1) |
| .PP |
| .B |
| Point3 nearseg3(Point3 p0, Point3 p1, Point3 testp) |
| .PP |
| .B |
| double pldist3(Point3 p, Point3 p0, Point3 p1) |
| .PP |
| .B |
| double vdiv3(Point3 a, Point3 b) |
| .PP |
| .B |
| Point3 vrem3(Point3 a, Point3 b) |
| .PP |
| .B |
| Point3 pn2f3(Point3 p, Point3 n) |
| .PP |
| .B |
| Point3 ppp2f3(Point3 p0, Point3 p1, Point3 p2) |
| .PP |
| .B |
| Point3 fff2p3(Point3 f0, Point3 f1, Point3 f2) |
| .PP |
| .B |
| Point3 pdiv4(Point3 a) |
| .PP |
| .B |
| Point3 add4(Point3 a, Point3 b) |
| .PP |
| .B |
| Point3 sub4(Point3 a, Point3 b) |
| .SH DESCRIPTION |
| These routines do arithmetic on points and planes in affine or projective 3-space. |
| Type |
| .B Point3 |
| is |
| .IP |
| .EX |
| .ta 6n |
| typedef struct Point3 Point3; |
| struct Point3{ |
| double x, y, z, w; |
| }; |
| .EE |
| .PP |
| Routines whose names end in |
| .B 3 |
| operate on vectors or ordinary points in affine 3-space, represented by their Euclidean |
| .B (x,y,z) |
| coordinates. |
| (They assume |
| .B w=1 |
| in their arguments, and set |
| .B w=1 |
| in their results.) |
| .TF reflect3 |
| .TP |
| Name |
| Description |
| .TP |
| .B add3 |
| Add the coordinates of two points. |
| .TP |
| .B sub3 |
| Subtract coordinates of two points. |
| .TP |
| .B neg3 |
| Negate the coordinates of a point. |
| .TP |
| .B mul3 |
| Multiply coordinates by a scalar. |
| .TP |
| .B div3 |
| Divide coordinates by a scalar. |
| .TP |
| .B eqpt3 |
| Test two points for exact equality. |
| .TP |
| .B closept3 |
| Is the distance between two points smaller than |
| .IR eps ? |
| .TP |
| .B dot3 |
| Dot product. |
| .TP |
| .B cross3 |
| Cross product. |
| .TP |
| .B len3 |
| Distance to the origin. |
| .TP |
| .B dist3 |
| Distance between two points. |
| .TP |
| .B unit3 |
| A unit vector parallel to |
| .IR p . |
| .TP |
| .B midpt3 |
| The midpoint of line segment |
| .IR pq . |
| .TP |
| .B lerp3 |
| Linear interpolation between |
| .I p |
| and |
| .IR q . |
| .TP |
| .B reflect3 |
| The reflection of point |
| .I p |
| in the segment joining |
| .I p0 |
| and |
| .IR p1 . |
| .TP |
| .B nearseg3 |
| The closest point to |
| .I testp |
| on segment |
| .IR "p0 p1" . |
| .TP |
| .B pldist3 |
| The distance from |
| .I p |
| to segment |
| .IR "p0 p1" . |
| .TP |
| .B vdiv3 |
| Vector divide \(em the length of the component of |
| .I a |
| parallel to |
| .IR b , |
| in units of the length of |
| .IR b . |
| .TP |
| .B vrem3 |
| Vector remainder \(em the component of |
| .I a |
| perpendicular to |
| .IR b . |
| Ignoring roundoff, we have |
| .BR "eqpt3(add3(mul3(b, vdiv3(a, b)), vrem3(a, b)), a)" . |
| .PD |
| .PP |
| The following routines convert amongst various representations of points |
| and planes. Planes are represented identically to points, by duality; |
| a point |
| .B p |
| is on a plane |
| .B q |
| whenever |
| .BR p.x*q.x+p.y*q.y+p.z*q.z+p.w*q.w=0 . |
| Although when dealing with affine points we assume |
| .BR p.w=1 , |
| we can't make the same assumption for planes. |
| The names of these routines are extra-cryptic. They contain an |
| .B f |
| (for `face') to indicate a plane, |
| .B p |
| for a point and |
| .B n |
| for a normal vector. |
| The number |
| .B 2 |
| abbreviates the word `to.' |
| The number |
| .B 3 |
| reminds us, as before, that we're dealing with affine points. |
| Thus |
| .B pn2f3 |
| takes a point and a normal vector and returns the corresponding plane. |
| .TF reflect3 |
| .TP |
| Name |
| Description |
| .TP |
| .B pn2f3 |
| Compute the plane passing through |
| .I p |
| with normal |
| .IR n . |
| .TP |
| .B ppp2f3 |
| Compute the plane passing through three points. |
| .TP |
| .B fff2p3 |
| Compute the intersection point of three planes. |
| .PD |
| .PP |
| The names of the following routines end in |
| .B 4 |
| because they operate on points in projective 4-space, |
| represented by their homogeneous coordinates. |
| .TP |
| pdiv4 |
| Perspective division. Divide |
| .B p.w |
| into |
| .IR p 's |
| coordinates, converting to affine coordinates. |
| If |
| .B p.w |
| is zero, the result is the same as the argument. |
| .TP |
| add4 |
| Add the coordinates of two points. |
| .PD |
| .TP |
| sub4 |
| Subtract the coordinates of two points. |
| .SH SOURCE |
| .B \*9/src/libgeometry |
| .SH "SEE ALSO |
| .IR matrix (3) |
