From 78e51a8c6678b6e3dff3d619aa786669f531f4bc Mon Sep 17 00:00:00 2001 From: rsc Date: Fri, 14 Jan 2005 03:45:44 +0000 Subject: checkpoint --- man/man3/quaternion.html | 163 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 163 insertions(+) create mode 100644 man/man3/quaternion.html (limited to 'man/man3/quaternion.html') diff --git a/man/man3/quaternion.html b/man/man3/quaternion.html new file mode 100644 index 00000000..257ebe52 --- /dev/null +++ b/man/man3/quaternion.html @@ -0,0 +1,163 @@ + +quaternion(3) - Plan 9 from User Space + + + + +
+
+
QUATERNION(3)QUATERNION(3) +
+
+

NAME
+ +
+ + qtom, mtoq, qadd, qsub, qneg, qmul, qdiv, qunit, qinv, qlen, slerp, + qmid, qsqrt – Quaternion arithmetic
+ +
+

SYNOPSIS
+ +
+ + +
+ + #include <draw.h> +
+ + #include <geometry.h> +
+ + Quaternion qadd(Quaternion q, Quaternion r) +
+ + Quaternion qsub(Quaternion q, Quaternion r) +
+ + Quaternion qneg(Quaternion q) +
+ + Quaternion qmul(Quaternion q, Quaternion r) +
+ + Quaternion qdiv(Quaternion q, Quaternion r) +
+ + Quaternion qinv(Quaternion q) +
+ + double qlen(Quaternion p) +
+ + Quaternion qunit(Quaternion q) +
+ + void qtom(Matrix m, Quaternion q) +
+ + Quaternion mtoq(Matrix mat) +
+ + Quaternion slerp(Quaternion q, Quaternion r, double a) +
+ + Quaternion qmid(Quaternion q, Quaternion r) +
+ + Quaternion qsqrt(Quaternion q)
+ +
+

DESCRIPTION
+ +
+ + The Quaternions are a non-commutative extension field of the Real + numbers, designed to do for rotations in 3-space what the complex + numbers do for rotations in 2-space. Quaternions have a real component + r and an imaginary vector component v=(i,j,k). Quaternions add + componentwise and multiply according to + the rule (r,v)(s,w)=(rs-v.w, rw+vs+vxw), where . and x are the ordinary + vector dot and cross products. The multiplicative inverse of a + non-zero quaternion (r,v) is (r,-v)/(r2-v.v). +
+ + The following routines do arithmetic on quaternions, represented + as
+ +
+ + typedef struct Quaternion Quaternion;
+ struct Quaternion{
+ +
+ + double r, i, j, k;
+ +
+ };
+ +
+ Name    Description
+ qadd    Add two quaternions.
+ qsub    Subtract two quaternions.
+ qneg    Negate a quaternion.
+ qmul    Multiply two quaternions.
+ qdiv    Divide two quaternions.
+ qinv    Return the multiplicative inverse of a quaternion.
+ qlen    Return sqrt(q.r*q.r+q.i*q.i+q.j*q.j+q.k*q.k), the length of + a quaternion.
+ qunit   Return a unit quaternion (length=1) with components proportional + to q’s. +
+ + A rotation by angle θ about axis A (where A is a unit vector) + can be represented by the unit quaternion q=(cos θ/2, Asin θ/2). + The same rotation is represented by -q; a rotation by -θ about -A + is the same as a rotation by θ about A. The quaternion q transforms + points by (0,x’,y’,z’) = q-1(0,x,y,z)q. Quaternion + multiplication composes rotations. The orientation of an object + in 3-space can be represented by a quaternion giving its rotation + relative to some ‘standard’ orientation. +
+ + The following routines operate on rotations or orientations represented + as unit quaternions:
+ mtoq    Convert a rotation matrix (see matrix(3)) to a unit quaternion.
+ qtom    Convert a unit quaternion to a rotation matrix.
+ slerp   Spherical lerp. Interpolate between two orientations. The + rotation that carries q to r is q-1r, so slerp(q, r, t) is q(q-1r)t.
+ qmid    slerp(q, r, .5)
+ qsqrt   The square root of q. This is just a rotation about the same + axis by half the angle.
+ +
+

SOURCE
+ +
+ + /usr/local/plan9/src/libgeometry/quaternion.c
+ +
+

SEE ALSO
+ +
+ + matrix(3), qball(3)
+ +
+ +

 +
+
+ + +
+
+
+Space Glenda +
+
+ + -- cgit v1.2.3