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Miloslav Ciz 2023-07-30 15:00:49 +02:00
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@ -4,7 +4,7 @@ Approximating means calculating or representing something with lesser than best
Using approximations however doesn't have to imply decrease in precision of the final result -- approximations very well serve [optimization](optimization.md). E.g. approximate metrics help in [heuristic](heuristic.md) algorithms such as [A*](a_star.md). Another use of approximations in optimization is as a quick preliminary check for the expensive precise algorithms: e.g. using bounding spheres helps speed up collision detection (if bounding spheres of two objects don't collide, we know they can't possibly collide and don't have to expensively check this).
Example of approximations:
Examples of approximations:
- **[Distances](distance.md)**: instead of expensive **Euclidean** distance (`sqrt(dx^2 + dy^2)`) we may use **Chebyshev** distance (`dx + dy`) or **Taxicab** distance (`max(dx,dy)`).
- **Engineering approximations** ("guesstimations"): e.g. **sin(x) = x** for "small" values of *x* or **pi = 3** (integer instead of float).
@ -14,4 +14,5 @@ Example of approximations:
- **[Ray tracing](ray_tracing.md)** neglects indirect lighting. Computer graphics in general is about approximating the solution of the rendering equation.
- **Real numbers** are practically always approximated with [floating point](floating_point.md) or [fixed point](fixed_point.md) (rational numbers).
- **[Numerical methods](numerical.md)** offer generality and typically yield approximate solutions while their precision vs speed can be adjusted via parameters such as number of iterations.
- **[Taylor series](taylor_series.md)** approximates given mathematical function and can be used to e.g. estimate solutions of [differential equations](differential_equation.md).
- **[Taylor series](taylor_series.md)** approximates given mathematical function and can be used to e.g. estimate solutions of [differential equations](differential_equation.md).
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