Translational Motion [\mathbf{v}(t^{[1]})=\mathbf{v}(t^{[0]})+\mathbf{M}^{-1}\int_{t^{[0]}}^{t^{[1]}}\mathbf{f}(\mathbf{x},\mathbf{v},t)dt] [\mathbf{x}(t^{[1]})=\mathbf{x}(t^{[0]})+\int_{t^{[0]}}...

Symmetric Positive Difiniteness (SPD) A is s.p.d. if and only if all of its eigenvalues are positive. In practice, eigenvalue decomposition is time-consuming. We choose diagonally dominant matrice...

The Texturing Pipeline Texturing is a technique for efficiently modeling variations in a surface’s material and finish. Texturing works by modifying the values used in the shading equation. The pix...

Display Encoding When we calculate the effect of lighting, texturing, or other operations, the values used are assumed to be linear. However, to avoid a variety of visual artifacts, display buffers...

Premultiplied Alphas and Compositing The over operator is also used for blending together photographs or synthetic renderings of objects. This process is called compositing. The image formed by th...

Transparency, Alpha, Compositing There are many different ways in which semitransparent objects can allow light to pass through them. For rendering algorithms, these can be roughly divided into: ...

Basics of Simulation Model and Simulation Collision Detection Determination Response Implementation Numerical Error ...

Aliasing & Antialiasing We will focus on what currently can be done in real time to alleviate aliasing artifacts. Sampling and Filtering Theory sampling theorem: For a signal to be sampled p...

Implement Shading Models In this section we will go over some key considerations for designing and writing implementations of shading and lighting equations. Frequency of Evaluation determine ...

Light Sources Punctual Light: A light source that is infinitely small and emits light in all directions. Point Light / Omni Light A point light is a light source that emits light in all...