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Supershapes (Superformula) Written by Paul Bourke March 2002 Based upon equations by Johan Gielis Intended as a modelling framework for natural forms. See also Superellipse The supershape equation is an extension of the both the equation of the sphere and ellipse
Converting a fisheye image into a panoramic, spherical or perspective projection Written by Paul Bourke November 2004, updated July 2016 The source code implementing the projections below is only available on request for a small fee. It includes a demo application and an invitation to convert an image of your choice to verify the code does what you seek. For more information please contact the aut
Points, lines, and planes In what follows are various notes and algorithms dealing with points, lines, and planes. This note describes the technique and gives the solution to finding the shortest distance from a point to a line or line segment. The equation of a line defined through two points P1 (x1,y1) and P2 (x2,y2) is
Can I use any data projector? No. The key requirement that a data projector needs to meet is focus. For a 60cm spherical mirror the projector needs to be able to focus to an image that is between 40 and 50cm wide. Unfortunately this is not something a projector manufacturer generally quotes since their clients don't normally want such a small image. The only way to be sure of a particular projecto
Discussed here are a number of interpolation methods, this is by no means an exhaustive list but the methods shown tend to be those in common use in computer graphics. The main attributes is that they are easy to compute and are stable. Interpolation as used here is different to "smoothing", the techniques discussed here have the characteristic that the estimated curve passes through all the given
MTL material format (Lightwave, OBJ) Excerpt from FILE FORMATS, Version 4.2 October 1995 Documentation created by: Diane Ramey, Linda Rose, and Lisa Tyerman Copyright 1995 Alias|Wavefront, Inc. All rights reserved 5. Material Library File (.mtl) Material library files contain one or more material definitions, each of which includes the color, texture, and reflection map of individual materials. Th
Introduction The following discusses computer based generation of stereo pairs as used to create a perception of depth. Such depth perception can be useful in many fields, for example, scientific visualisation, entertainment, games, appreciation of architectural spaces, etc. Depth cues There are a number of cues that the human visual system uses that result in a perception of depth. Some of these
Attributed to Cliff Pickover Graphics by Paul Bourke February 2004 See also Peter de Jong attractors Contribution by Paul Richards including source code. Definition xn+1 = sin(a yn) + c cos(a xn) yn+1 = sin(b xn) + d cos(b yn) where a, b, c, d are variables that define each attractor. a = -1.4, b = 1.6, c = 1.0, d = 0.7 a = 1.6, b = -0.6, c = -1.2, d = 1.6 a = 1.7, b = 1.7, c = 0.6, d = 1.2 a = 1.
Self Similarity Fractals are usually associated with self similarity across scales. For pure/idealised mathematical fractals the self similarity may be across an infinite range of scales, such as the Sierpinski Gasket. In real life and in nature the self similarity is only across a range of scales. Branching structures, such as most of the examples shown here, are classic examples of self similari
P a u l B o u r k e Search: paulbourke.net − +61 (0)433338325 − paul.bourke@gmail.com − FB − Sketchfab − YouTube − Vimeo − Shapeways If you have found the contents of this site useful, please donate to one of my vices: Cup of coffee − Can of beer − Bottle of wine Fractals, Chaos, Self-Similarity The following is a collection of fractal, chaos and attractors by the author. It includes most known
Written by Paul Bourke Assistance by Roberto Calati, and panoramic images by Peter Murphy March 2004 Chinese version: InfoAV China, November 2004. Implementation for Quartz Composer contributed by Matthias Oostrik: seb.zip. Includes a Core Image Filter and an example composition for a three projector display using a Matrox Triplehead2Go. Introduction There are a number of applications which ben
The following illustrates a technique of iteratively tiling the plane with non-overlapping shapes where, on each iteration, the position is determined randomly and the area is some decreasing function. Note that the shapes, when circles, are not added as "Soddy" circles as in Apollonian [3] space filling fractals, nor do they even need to touch at a single point of another shape [4]. If the area o
Introduction TGA or TARGA format is a format for describing bitmap images, it is capable of representing bitmaps ranging from black and white, indexed colour, and RGB colour, the format also supports various compression methods. This note describes the minimal requirements for creating a TGA file for a 24 bit RGB uncompressed colour image, this covers most applications where a developer might want
P a u l B o u r k e Search: paulbourke.net − +61 (0)433338325 − paul.bourke@gmail.com − FB − Sketchfab − YouTube − Vimeo − Shapeways If you have found the contents of this site useful, please donate to one of my vices: Cup of coffee − Can of beer − Bottle of wine The following is a random collection of various topics in geometry the author has explored or simply documented over the years. Many
Also known as: "3D Contouring", "Marching Cubes", "Surface Reconstruction" Written by Paul Bourke May 1994 Based on tables by Cory Gene Bloyd along with additional example source code marchingsource.cpp An alternative table by Geoffrey Heller. rchandra.zip: C++ classes contributed by Raghavendra Chandrashekara. OpenGL source code, sample volume: cell.gz (old) volexample.zip: An example showing how
Also known as the Stanford Triangle Format Source code examples: ply.h, plytest.c, plyfile.c, plydocs.txt Example of an ascii ply file Introduction This document presents the PLY polygon file format, a format for storing graphical objects that are described as a collection of polygons. Our goal is to provide a format that is simple and easy to implement but that is general enough to be useful for
The following describes how to transform a standard lens distorted image into what one would get with a perfect perspective projection (pin-hole camera). Alternatively it can be used to turn a perspective projection into what one would get with a lens. To illustrate the type of distortion involved consider a reference grid, with a 35mm lens it would look something line the image on the left, a tra
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