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) Distance between a point, a line and a plane The intersection of a line with another line (2D) The closest line between two lines (3D) The intersection of a line with a plane Mathematics describing a plane The intersection of two planes The intersection of three planes Polygon area and centroid calculation Inside / outside polygon test Reflection of a ray Direction Cosines Eulers number and closed surfaces Determining whether a line segment intersects a facet Coordinate transformations on the plane (2D) Cartesian, Cylindrical, and Spherical Euler angles and coordinate transformations Converting between left and right coordinate systems Clipping a line with a polygon Clockwise test for polygons in 2D Test for concave/convex polygon in 2D Area of (planar) polygons in 3D Spheres, equations and terminology The intersection of a line and a sphere (or a circle) Equation of the circle through 3 points Equation of the sphere through 4 points Intersecting area of circles on a plane Rotation of a point about an arbitrary axis Creating a plane/disk perpendicular to a line segment Intersection of two circles on the plane Circumference of an ellipse Intersection of two spheres Distributing Points on a Sphere Quadric equations in x and y of degree 2 Fowler angles: Comparing angles without trigonometry 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 Including Anamorphic projections and 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.