qball(9) [plan9 man page]

QBALL(9.2)																QBALL(9.2)

NAME

       qball - 3-d rotation controller

SYNOPSIS

       #include <libg.h>

       #include <geometry.h>

       void qball(Rectangle r, Mouse *mousep,
	    Quaternion *orientation,
	    void (*redraw)(void), Quaternion *ap)

DESCRIPTION

       Qball  is an interactive controller that allows arbitrary 3-space rotations to be specified with the mouse.  Imagine a sphere with its cen-
       ter at the midpoint of rectangle r, and diameter the smaller of r's dimensions.	Dragging from one point on the sphere to another specifies
       the  endpoints  of  a  great-circle  arc.  (Mouse points outside the sphere are projected to the nearest point on the sphere.)  The axis of
       rotation is normal to the plane of the arc, and the angle of rotation is twice the angle of the arc.

       Argument mousep is a pointer to the mouse event that triggered the interaction.	It should have some button  set.   Qball  will	read  more
       events into mousep, and return when no buttons are down.

       While  qball is reading mouse events, it calls out to the caller-supplied routine redraw, which is expected to update the screen to reflect
       the changing orientation.  Argument orientation is the orientation that redraw should  examine,	represented  as  a  unit  Quaternion  (see
       quaternion(9.2)).   The caller may set it to any orientation.  It will be updated before each call to redraw (and on return) by multiplying
       by the rotation specified with the mouse.

       It is possible to restrict qball's attention to rotations about a particular axis.  If ap is null, the rotation is  unconstrained.   Other-
       wise,  the  rotation will be about the same axis as *ap.  This is accomplished by projecting points on the sphere to the nearest point also
       on the plane through the sphere's center and normal to the axis.

SOURCE

       /sys/src/libgeometry/qball.c

SEE ALSO

       quaternion(9.2)
       Ken Shoemake, ``Animating Rotation with Quaternion Curves'', SIGGRAPH '85 Conference Proceedings.

																	QBALL(9.2)

QUATERNION(9.2) 														   QUATERNION(9.2)

NAME

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

SYNOPSIS

       #include <libg.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	component-
       wise  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 0 about axis A (where A is a unit vector) can be represented by the unit quaternion q=(cos 0/2, Asin  0/2).	 The  same
       rotation  is  represented  by  -q; a rotation by -0 about -A is the same as a rotation by 0 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 tstack(9.2)) 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

       /sys/src/libgeometry/quaternion.c

SEE ALSO

       tstack(9.2), qball(9.2)

																   QUATERNION(9.2)