From adc93f6097615f16d57e8a24a256302f2144ec4e Mon Sep 17 00:00:00 2001 From: rsc Date: Fri, 14 Jan 2005 17:37:50 +0000 Subject: cut out the html - they're going to cause diffing problems. --- man/man3/matrix.html | 263 --------------------------------------------------- 1 file changed, 263 deletions(-) delete mode 100644 man/man3/matrix.html (limited to 'man/man3/matrix.html') diff --git a/man/man3/matrix.html b/man/man3/matrix.html deleted file mode 100644 index ad72d10a..00000000 --- a/man/man3/matrix.html +++ /dev/null @@ -1,263 +0,0 @@ - -matrix(3) - Plan 9 from User Space - - - - -
-
-
MATRIX(3)MATRIX(3) -
-
-

NAME
- -
- - ident, matmul, matmulr, determinant, adjoint, invertmat, xformpoint, - xformpointd, xformplane, pushmat, popmat, rot, qrot, scale, move, - xform, ixform, persp, look, viewport – Geometric transformations
- -
-

SYNOPSIS
- -
- - -
- - #include <draw.h> -
- - #include <geometry.h> -
- - void ident(Matrix m) -
- - void matmul(Matrix a, Matrix b) -
- - void matmulr(Matrix a, Matrix b) -
- - double determinant(Matrix m) -
- - void adjoint(Matrix m, Matrix madj) -
- - double invertmat(Matrix m, Matrix inv) -
- - Point3 xformpoint(Point3 p, Space *to, Space *from) -
- - Point3 xformpointd(Point3 p, Space *to, Space *from) -
- - Point3 xformplane(Point3 p, Space *to, Space *from) -
- - Space *pushmat(Space *t) -
- - Space *popmat(Space *t) -
- - void rot(Space *t, double theta, int axis) -
- - void qrot(Space *t, Quaternion q) -
- - void scale(Space *t, double x, double y, double z) -
- - void move(Space *t, double x, double y, double z) -
- - void xform(Space *t, Matrix m) -
- - void ixform(Space *t, Matrix m, Matrix inv) -
- - int persp(Space *t, double fov, double n, double f) -
- - void look(Space *t, Point3 eye, Point3 look, Point3 up) -
- - void viewport(Space *t, Rectangle r, double aspect)
- -
-

DESCRIPTION
- -
- - These routines manipulate 3-space affine and projective transformations, - represented as 4×4 matrices, thus:
- -
- - typedef double Matrix[4][4];
- -
- - -
- Ident stores an identity matrix in its argument. Matmul stores - a×b in a. Matmulr stores b×a in b. Determinant returns the determinant - of matrix m. Adjoint stores the adjoint (matrix of cofactors) - of m in madj. Invertmat stores the inverse of matrix m in minv, - returning m’s determinant. Should m be singular - (determinant zero), invertmat stores its adjoint in minv. -
- - The rest of the routines described here manipulate Spaces and - transform Point3s. A Point3 is a point in three-space, represented - by its homogeneous coordinates:
- -
- - typedef struct Point3 Point3;
- struct Point3{
- -
- - double x, y, z, w;
- -
- };
- -
- - -
- The homogeneous coordinates (x, y, z, w) represent the Euclidean - point (x/w, y/w, z/w) if w!=0, and a “point at infinity” if w=0. - -
- - A Space is just a data structure describing a coordinate system:
- -
- - typedef struct Space Space;
- struct Space{
- -
- - Matrix t;
- Matrix tinv;
- Space *next;
- -
- };
- -
- - -
- It contains a pair of transformation matrices and a pointer to - the Space’s parent. The matrices transform points to and from - the “root coordinate system,” which is represented by a null Space - pointer. -
- - Pushmat creates a new Space. Its argument is a pointer to the - parent space. Its result is a newly allocated copy of the parent, - but with its next pointer pointing at the parent. Popmat discards - the Space that is its argument, returning a pointer to the stack. - Nominally, these two functions define a stack of - transformations, but pushmat can be called multiple times on the - same Space multiple times, creating a transformation tree. -
- - Xformpoint and Xformpointd both transform points from the Space - pointed to by from to the space pointed to by to. Either pointer - may be null, indicating the root coordinate system. The difference - between the two functions is that xformpointd divides x, y, z, - and w by w, if w!=0, making (x, y, z) the Euclidean - coordinates of the point. -
- - Xformplane transforms planes or normal vectors. A plane is specified - by the coefficients (a, b, c, d) of its implicit equation ax+by+cz+d=0. - Since this representation is dual to the homogeneous representation - of points, libgeometry represents planes by Point3 structures, - with (a, b, c, d) stored in (x, y, z, w). -
- - The remaining functions transform the coordinate system represented - by a Space. Their Space * argument must be non-null -- you can’t - modify the root Space. Rot rotates by angle theta (in radians) - about the given axis, which must be one of XAXIS, YAXIS or ZAXIS. - Qrot transforms by a rotation about an - arbitrary axis, specified by Quaternion q. -
- - Scale scales the coordinate system by the given scale factors - in the directions of the three axes. Move translates by the given - displacement in the three axial directions. -
- - Xform transforms the coordinate system by the given Matrix. If - the matrix’s inverse is known a priori, calling ixform will save - the work of recomputing it. -
- - Persp does a perspective transformation. The transformation maps - the frustum with apex at the origin, central axis down the positive - y axis, and apex angle fov and clipping planes y=n and y=f into - the double-unit cube. The plane y=n maps to y’=-1, y=f maps to - y’=1. -
- - Look does a view-pointing transformation. The eye point is moved - to the origin. The line through the eye and look points is aligned - with the y axis, and the plane containing the eye, look and up - points is rotated into the x-y plane. -
- - Viewport maps the unit-cube window into the given screen viewport. - The viewport rectangle r has r.min at the top left-hand corner, - and r.max just outside the lower right-hand corner. Argument aspect - is the aspect ratio (dx/dy) of the viewport’s pixels (not of the - whole viewport). The whole window is transformed - to fit centered inside the viewport with equal slop on either - top and bottom or left and right, depending on the viewport’s - aspect ratio. The window is viewed down the y axis, with x to - the left and z up. The viewport has x increasing to the right - and y increasing down. The window’s y coordinates are mapped, - unchanged, into the viewport’s z coordinates.
- -
-

SOURCE
- -
- - /usr/local/plan9/src/libgeometry/matrix.c
- -
-

SEE ALSO
- -
- - arith3(3)
- -
- -

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