Bump Mapping This section describes a large family of small-scale detail representation techniques that we collectively call bump mapping. All these methods are typically implemented by modifying t...

Alpha Mapping This section discusses the use of textures with alphas, noting various limitations and solutions along the way. Decal By assigning an alpha of 0 to a texel, you make it transparent...

Material Mapping A common use of a texture is to modify a material property affecting the shading equation. Real-world objects usually have material properties that vary over their surface. To sim...

Texture Animation The image applied to a surface does not have to be static. For example, a video source can be used as a texture that changes from frame to frame. The texture coordinates need no...

Procedural Texturing Although procedural textures are commonly used in offline rendering applications, image textures are far more common in real-time rendering. This is due to the extremely high e...

Image Texturing What the floating point coordinates of the center of a pixel are? DirectX 10 onward changes to OpenGL’s system, where the center of a texel has the fractional values (0.5,0.5)—...

Particle Collision Detection and Response Concept: Signed Distance Field (omitted) The corresponding operation of AND bool operation is [inside: \phi(\mathbf{x}) = \max {\phi_i(\mathbf{x})}] O...

A Mass-Spring System We could turn the mesh plane into a mass-spring system to simulate the cloth. But first, we need to make raw mesh data into a data structure for simulation. Topological Const...

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...