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Clipping, in the context of computer graphics, is a method to selectively enable or disable rendering operations within a defined region of interest.Mathematically, clipping can be described using the terminology of constructive geometry.
A basic 3D rotation (also called elemental rotation) is a rotation about one of the axes of a coordinate system. The following three basic rotation matrices rotate vectors by an angle θ about the x-, y-, or z-axis, in three dimensions, using the right-hand rule—which codifies their alternating signs.
One or more concave polygons may produce more than one intersecting polygon. Convex polygons will only have one intersecting polygon. The same algorithm can be used for merging two polygons by starting at the outbound intersections rather than the inbound ones. However this can produce counter-clockwise holes. Some polygon combinations may be ...
Polygon Mesh Processing by Mario Botsch et al. is a textbook on the topic of Geometry Processing. [1]Geometry processing is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation and transmission of complex 3D models.
In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO(3) , the group of all rotation matrices ...
Again using the example of rendering double-sided polygons using the painter's algorithm, to draw a polygon P correctly requires that all polygons behind the plane P lies in must be drawn first, then polygon P, then finally the polygons in front of P. If this drawing order is satisfied for all polygons in a scene, then the entire scene renders ...
On the left a model without back-face culling; on the right the same model with back-faces removed. Because the polygons do not form a closed solid, differences can be seen. In computer graphics, back-face culling determines whether a polygon that is part of a solid needs to be drawn.
By a reduction of the model's associated state space dimension or degrees of freedom, an approximation to the original model is computed which is commonly referred to as a reduced order model. Reduced order models are useful in settings where it is often unfeasible to perform numerical simulations using the complete full order model.
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