From 78e51a8c6678b6e3dff3d619aa786669f531f4bc Mon Sep 17 00:00:00 2001 From: rsc Date: Fri, 14 Jan 2005 03:45:44 +0000 Subject: checkpoint --- man/man3/matrix.html | 263 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 263 insertions(+) create mode 100644 man/man3/matrix.html (limited to 'man/man3/matrix.html') diff --git a/man/man3/matrix.html b/man/man3/matrix.html new file mode 100644 index 00000000..ad72d10a --- /dev/null +++ b/man/man3/matrix.html @@ -0,0 +1,263 @@ + +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