vsr::cga::Construct Struct Reference

constructive syntactic sugar for making geometric elements More...

#include <vsr_cga3D_op.h>

Static Public Member Functions
static Pair	pair (const DualSphere &s, const Vec &v)
	constructs a Pair on Sphere s in v direction More...
static Pair	pair (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z, Vec vec=Vec::y, VSR_PRECISION r=1.0)
	Point Pair at x,y,z with direction vec (default Y) and radius r (default 1)
static Point	pointA (const Pair &pp)
	First point of point pair pp.
static Point	pointB (const Pair &pp)
	Second point of point pair pp.
static Point	point (const Circle &c, VSR_PRECISION t)
	Point on Circle at theta t.
static Point	point (const DualSphere &s, const Vec &v)
	Point on Sphere in v direction.
static Point	point (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z)
	Point from x,y,z.
static Point	point (const Vec &v)
	Point from vec.
static Point	point (const Line &, const Point &)
	Point on line l closest to p.
static Point	point (const DualLine &, const Point &)
	Point on dualline l closest to p.
static Circle	circle (const Point &a, const Point &b, const Point &c)
	Circle through three points.
static Circle	circle (const Point &p, VSR_PRECISION r, const Biv &biv=Biv::xy)
	Circle at point p with radius r, facing direction biv.
static Circle	circle (const Biv &B)
	Circle at origin in plane of bivector B.
static Circle	circle (const Vec &v, VSR_PRECISION r=1.0)
static Circle	circle (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z, Biv biv=Biv::xy, VSR_PRECISION r=1.0)
static Sphere	sphere (const Pnt &a, const Pnt &b, const Pnt &c, const Pnt &d)
static DualSphere	sphere (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z, VSR_PRECISION r=1.0)
static DualSphere	sphere (const Point &p, VSR_PRECISION r=1.0)
static DualPlane	plane (VSR_PRECISION a, VSR_PRECISION b, VSR_PRECISION c, VSR_PRECISION d=0.0)
	Dual plane with normal and distance from center.
static DualPlane	plane (const Vec &v, VSR_PRECISION d=0.0)
	Dual plane from vec and distance from center.
static Plane	plane (const Pnt &a, const Pnt &b, const Pnt &c)
	Direct plane through three points.
static DualLine	axis (const Cir &c)
	DualLine axis of circle c.
static Line	line (const Vec &a, const Vec &b)
	Direct line through points a and b.
static Line	line (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z)
	Direct line through origin.
static Line	dualLine (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z)
	Dual line through origin.
static Line	line (const Point &a, const Point &b)
	Direct line through two points.
static Line	line (const Point &a, const Vec &b)
	Direct line through point a in direction b.
static Circle	hline (const Point &a, const Point &b)
	Hyperbolic line through two points.
static Circle	sline (const Point &a, const Point &b)
	Spherical line through two points.
static VSR_PRECISION	distance (const Lin &lin, const Pnt &pnt)
	Squared Distance between a line and a point.
static Circle	meet (const Dls &s, const Dls &d)
	circle intersection of dual spheres
static Circle	meet (const Dls &s, const Dlp &d)
	circle intersection of dual sphere and direct plane
static Circle	meet (const Dls &s, const Pln &d)
	circle intersection of dual spehre and direct plane
static Circle	meet (const Sphere &s, const DualPlane &d)
	circle intersection of direct sphere and dual plane
static Circle	meet (const Sphere &s, const Plane &d)
	circle intersection of direct sphere and direct plane
static Point	meet (const Line &lin, const DualPlane &)
	normalized and nulled point intersection of line and dual plane
static Point	meet (const DualLine &, const DualPlane &)
	normalized and nulled point intersection of dualline and dual plane
static Point	meet (const Line &la, const Line &lb)
	Point intersection of two lines.
static Pair	meet (const Cir &cir, const Dlp &dlp)
	point pair intersection of circle and Dual plane
static Pair	meet (const Cir &cir, const Dls &s)
	point pair intersection of circle and Dual sphere
static bool	hit (const Point &, const Pair &)
	hit tests between point and pair (treats pair as an "edge")
static bool	hit (const Point &, const Circle &)
	hit tests between point and circle (treats circle as "disc")
static double	squaredDistance (const Point &a, const Point &b)
static Point	hnorm (const Pnt &p)
	hyperbolic normalization of a conformal point
static double	hdist (const Pnt &pa, const Pnt &pb)
	hyperbolic distance between two conformal points
static Pair	hgen (const Pnt &pa, const Pnt &pb, double amt)
	hyperbolic translation transformation generator between two conformal points
static Point	hspin (const Pnt &pa, const Pnt &pb, double amt)
	hyperbolic spin transformation from pa to pb by amt (0,1)
template<class A , class B >
static Point	affine (const A &a, const B &b, VSR_PRECISION t)

Detailed Description

constructive syntactic sugar for making geometric elements

if we are in namespace cga we can just write

Construct::point(x,y,z) 

or to help create a generic generator

Construct::gen( <some bivector element> )

Member Function Documentation

static Pair vsr::cga::Construct::pair ( const DualSphere &  s, const Vec &  v  )

static

constructs a Pair on Sphere s in v direction

Parameters

s	vsr::cga::DualSphere;
v	vsr::cga::Vec;

Returns

vsr::cga::Pair;

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The documentation for this struct was generated from the following file:

• /Users/wolftype/code/versor/vsr/space/vsr_cga3D_op.h