They simplify and unify the mathematics used in graphics: They allow you to represent translations with matrices. They allow you to represent the division by depth in perspective projections. The ...

The classic book Computer Graphics: Principles and Practice (second edition) by Foley, van Dam, et al. describes such an algorithm in section 19.2. The explanation in the book seems to come from an ...

When modeling parametric surfaces with a mesh in the parameter domain, T-junctions will most probably appear as discontinuities in the surface. These will show up as gaps in the rendering. See below. ...

You have an instance of a problem called curve reconstruction from unorganized points. Now that you know what to search for you'll find several methods, such as the crust, NN-crust, etc. Here are a ...

The general problem is called graph drawing and is not an easy problem. The graphs that can be drawn on the plane without crossings are called planar, but not all graphs are planar: the typical graphs ...

One solution is bilinear mapping, which works for every convex quadrilateral. Let $A, B, C, D$ be the vertices of a quadrilateral $Q$ in the plane, in this order. Then \$f(u,v)=(1-u)(1-v)A + u(1-v)B +...

Choose the color RGB of your colorful glasses and choose how transparent they are by choosing an alpha value A. Then alpha composite the glasses on top of the input image: OutputR = R * A + InputR * (...

Try -trim instead of -shave: convert original.png -trim trimmed.png See the docs for this and other options.

A good starting point is the classic paper Using particles to sample and control implicit surfaces, published in SIGGRAPH 1994. A simple particle simulation described in the paper Sampling implicit ...