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Scene rendered with RRV [1] (simple implementation of radiosity renderer based on OpenGL) 79th iteration The Cornell box, rendered with and without radiosity by BMRT. In 3D computer graphics, radiosity is an application of the finite element method to solving the rendering equation for scenes with surfaces that reflect light diffusely.
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
Symbolic differentiation faces the difficulty of converting a computer program into a single mathematical expression and can lead to inefficient code. Numerical differentiation (the method of finite differences) can introduce round-off errors in the discretization process and cancellation. Both of these classical methods have problems with ...
It extends the classical finite element method by enriching the solution space for solutions to differential equations with discontinuous functions. Extended finite element methods enrich the approximation space to naturally reproduce the challenging feature associated with the problem of interest: the discontinuity, singularity, boundary layer ...
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are polygons, meshes, and simplicial complexes. It is used in the study of computer graphics and topological combinatorics. Topics in this area include: Discrete Laplace operator; Discrete ...
In computer graphics, free-form deformation (FFD) is a geometric technique used to model simple deformations of rigid objects. It is based on the idea of enclosing an object within a cube or another hull object, and transforming the object within the hull as the hull is deformed.
In computer graphics, a line drawing algorithm is an algorithm for approximating a line segment on discrete graphical media, such as pixel-based displays and printers. On such media, line drawing requires an approximation (in nontrivial cases). Basic algorithms rasterize lines in one color.
They are most commonly found in computer simulations, e.g. for computational fluid dynamics in the context of scientific and engineering applications. Other notable examples include solving partial differential equations , [ 1 ] the Jacobi kernel, the Gauss–Seidel method , [ 2 ] image processing [ 1 ] and cellular automata . [ 3 ]