Geometry

POV-Ray: A Tool for Creating Engaging Visualisation of Geometry Various notes on polygons and meshes Includes Surface (polygon) simplification, Clipping a polygonal facet with an arbitrary plane, Surface Relaxation and Smoothing of polygonal data, Mesh crumpling, splitting polygons, two sided facets, polygon types.

Philosophy is written in this grand book - I mean universe - which stands continuously open to our gaze, but which cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth.
Galileo (1623)

Contouring Algorithm Description of an efficient contouring algorithm as it appeared in Byte magazine. (Byte Magazine, 1987) and a more general approach for arbitrary contour planes and polygonal meshes.

Spherical projections Methods for mapping points on a spherical surface onto a plane, stereographic and cylindrical (including Mercator) projections. Includes Aitoff map projection: Conversion to/from longitude/latitude (spherical map) Projection types Classification of projections from 3D to 2D and specific examples of oblique projections.

A triangle was an improvement to the square wheel. It eliminated one bump.
BC comics

Planar (stretching) distortion in the plane Anamorphic projections Mappings in the complex plane Otherwise known as Conformal maps

Polygonising a scalar field Otherwise known as marching cubes and marching tetrahedrons. HyperSpace (Historic) A Macintosh 4 dimensional geometry viewer and manual.

There are holes in the sky. Where the rain gets in. But they're ever so small. That's why the rain is thin.
Spike Milligan

Waterman Polyhedra	Cylinder intersections	Plexagons (Pleated hexagon)	4D platonic solids	Polar Sphere
"We should make things as simple as possible, but not simpler." Albert Einstein
Coordinates for 4D polyhedra	Polar + Star	Parallelohedron	Platonic solids	Time Star
To see a World in a Grain of Sand, And Heaven in a Wild Flower Hold Infinity in the palm of your hand, And Eternity in an hour William Blake
Photos by Gayla Chandler	Star Sphere	Build your own	80 Polyhedra	Cube personalities
If triangles had a God, He'd have three sides. Old Yiddish proverb
	Rhombic Triacontahedron	Polyhedra data files	Kissing number
Experience hath shewn, that even under the best forms of government those entrusted with power have, in time, and by slow operations, perverted it into tyranny. Thomas Jefferson

New   Stereo projection for hemispherical domes Unity game engine and iDome Data visualisation in crystal Warping patch for Quartz Composer FAQ: Spherical mirror projection for hemispherical domes
Index Papers, Articles, Seminars Exhibitions Projection Data Formats Fractals, Chaos Surfaces, Curves Modelling, Rendering Texture, Colour Geometry Fun, puzzles Other Old stuff
The contents of this web site are © Copyright Paul Bourke or a third party contributer where indicated. You may print or save an electronic copy of parts of this web site for your own personal use. Permission must be sought for any other use.