ref: ec73849b6936d839410ccb239d14b2f7c7ca3d6f
dir: /sys/src/libgeometry/rframe.c/
#include <u.h>
#include <libc.h>
#include <geometry.h>
/*
* implicit identity origin rframes
*
* static RFrame IRF2 = {
* .p = {0,0,1},
* .bx = {1,0,0},
* .by = {0,1,0},
* };
*
* static RFrame3 IRF3 = {
* .p = {0,0,0,1},
* .bx = {1,0,0,0},
* .by = {0,1,0,0},
* .bz = {0,0,1,0},
* };
*
* these rframes are used on every xform to keep the points in the
* correct plane (i.e. with proper w values); they are written here as a
* reference for future changes. the bases are ignored since they turn
* into an unnecessary identity xform.
*
* the implicitness comes from the fact that using the _irf* filters
* makes the rframexform equivalent to:
* rframexform(invrframexform(p, IRF), rf);
* and the invrframexform to:
* rframexform(invrframexform(p, rf), IRF);
*/
static Point2
_irfxform(Point2 p)
{
p.w--;
return p;
}
static Point2
_irfxform⁻¹(Point2 p)
{
p.w++;
return p;
}
static Point3
_irfxform3(Point3 p)
{
p.w--;
return p;
}
static Point3
_irfxform3⁻¹(Point3 p)
{
p.w++;
return p;
}
Point2
rframexform(Point2 p, RFrame rf)
{
Matrix m = {
rf.bx.x, rf.by.x, 0,
rf.bx.y, rf.by.y, 0,
0, 0, 1,
};
invm(m);
return xform(subpt2(_irfxform⁻¹(p), rf.p), m);
}
Point3
rframexform3(Point3 p, RFrame3 rf)
{
Matrix3 m = {
rf.bx.x, rf.by.x, rf.bz.x, 0,
rf.bx.y, rf.by.y, rf.bz.y, 0,
rf.bx.z, rf.by.z, rf.bz.z, 0,
0, 0, 0, 1,
};
invm3(m);
return xform3(subpt3(_irfxform3⁻¹(p), rf.p), m);
}
Point2
invrframexform(Point2 p, RFrame rf)
{
Matrix m = {
rf.bx.x, rf.by.x, 0,
rf.bx.y, rf.by.y, 0,
0, 0, 1,
};
return _irfxform(addpt2(xform(p, m), rf.p));
}
Point3
invrframexform3(Point3 p, RFrame3 rf)
{
Matrix3 m = {
rf.bx.x, rf.by.x, rf.bz.x, 0,
rf.bx.y, rf.by.y, rf.bz.y, 0,
rf.bx.z, rf.by.z, rf.bz.z, 0,
0, 0, 0, 1,
};
return _irfxform3(addpt3(xform3(p, m), rf.p));
}