nklein software---products/rt

-- N-Dimensional Ray Tracing

The picture at the top of the page is a trace of a 4-dimensional cube with a cylinder cut out of each major axis.

Here is a sample of the objects and textures that are possible with this raytracer. This is a slice from a trace of a four-dimensional scene. Here is the whole trace and the source file that generated it.

From left to right, these are:

a (0,4)-cylinder (cube)
a (2,4)-cylinder
a (3,4)-cylinder
a (4,4)-cylinder (hypersphere)
a duo-circle
a quadratic surface (intersected with a box)
a half-space (intersected with a box)
a simplex
a hypercube (8-cell)
a hyperoctahedron (16-cell)
a 24-cell
a 120-cell
a 600-cell
a union of a cube and a sphere
the intersection of a cube and a sphere
the intersection of a cube and the complement of a sphere
an extrusion of a hexagon into 4-d
a refracting half-sphere over a striped box
a (3-4)-cylinder that is colored by tracing back into this same scene

Here, a (k,n)-cylinder means an n-dimensional cylinder where k of the dimensions are restricted by the sum of their squares being less than or equal to the square of the radius. The remaining (n-k) dimensions are independently clipped.

Feedback of any sort is welcome to rt@nklein.com

v2.7.2007.05.17

Latest version fixes template classes to be compatible with newer compilers.

The documentation

The source code

Feature set now includes:

Phong shading, reflection, refraction
Functional textures (including textures generated by raytracing other scenes)
Cylinders (including spheres and cubes)
Quadratic surfaces
Regular polytopes
Halfspaces
Convex hulls of a sets of points
Extrusions of lower-dimensional objects
Intersections, unions, and complements
Different colors for k-dimensional subfacets of convex hulls and coxeter polytopes

Here are some sample images:

A stereo pair of slices of some 24-cells with the input file. The vertexes (0-facets) are pink, the edges (1-facets) are dark gray, the faces (2-facets) are yellowish, and the facets (3-facets) are green.
Some 3-D Polytopes with edges and vertexes colored differently and the input file
Some 3-D Polytopes and the input file
Some spheres positioned so that the image can only work because the raytracing is done in four dimensions. Here, a blue unit sphere is at [ 0, 2, 0, 0 ], a green unit sphere is at [ 0, 0, 2, 0 ], and a red unit sphere is at [ 0, 0, 0, 2 ]. The viewpoint is from along the negative x-axis toward the origin. There is a reflective unit sphere at [ 2.0761204674887133, 0, 0, -0.3826834323650898 ] that lets you see the reflection of the red sphere even though this slice is entirely the w = 0 slice. Here's the input file. And, here is a stereo pair of a more complete trace of the same scene. And, here is a composite image trying to show what the full 3-d retina looks like and the same with the sky removed.
The 600-cell and its input file
An animation of a hypercube rotating in various ways and another
An animation of a 5-d hypercube rotating in various ways
An animation of three (differently-oriented) duo-circles (take a circle in the x-y plane and a circle in the z-w plane and extrude each out to four-dimensions... then intersect the two shapes) rotating in various ways and the animation script used. Here's the same rotation sequence with three duo-circles again. The top one has a radially striped x-y circle. The bottom one has a radially striped z-w circle. The center one has both.
An animation of a rotating hypersphere with colors banded to show polar coordinates on the surface and the animation script used
The same animation except with axis-aligned (3,4)-cylinders and the animation script used
Slides from a presentation on the raytracer. Unfortunately, the bookmarks get scrogged by the interleaved pages of notes. And, here are all of the input files that went into that presentation.
An animation of a rotating 24-cell (you may have to download it and play it from a file) and the animation script used

Here is the source for a utility used to create frames for animation from a simple script of rotations and a template file. The script tells the number of frames in the animation. After that, each line tells which plane to rotate parallel to, the starting angle, ending angle, starting frame, and ending frame.

Off-site links about N-Dimensional Stuff