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