f2dc2027f6
in the original GitHub fork: https://github.com/ntoronto/racket Some things about this are known to be broken (most egregious is that the array tests DO NOT RUN because of a problem in typed/rackunit), about half has no coverage in the tests, and half has no documentation. Fixes and docs are coming. This is committed now to allow others to find errors and inconsistency in the things that appear to be working, and to give the author a (rather incomplete) sense of closure.
64 lines
1.8 KiB
Racket
64 lines
1.8 KiB
Racket
#lang typed/racket/base
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(require math/matrix)
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(provide matrix-2d-rotation
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matrix-2d-scaling
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matrix-2d-shear-x
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matrix-2d-shear-y
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matrix-2d-reflection
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matrix-2d-orthogonal-projection)
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; Transformations from:
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; http://en.wikipedia.org/wiki/Transformation_matrix
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(: matrix-2d-rotation : Real -> (Matrix Number))
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; matrix representing rotation θ radians counter clockwise
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(define (matrix-2d-rotation θ)
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(define cosθ (cos θ))
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(define sinθ (sin θ))
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(matrix/dim 2 2
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cosθ (- sinθ)
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sinθ cosθ))
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(: matrix-2d-scaling : Real Real -> (Matrix Number))
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(define (matrix-2d-scaling sx sy)
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(matrix/dim 2 2
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sx 0
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0 sy))
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(: matrix-2d-shear-x : Real -> (Matrix Number))
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(define (matrix-2d-shear-x k)
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(matrix/dim 2 2
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1 k
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0 1))
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(: matrix-2d-shear-y : Real -> (Matrix Number))
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(define (matrix-2d-shear-y k)
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(matrix/dim 2 2
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1 0
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k 1))
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(: matrix-2d-reflection : Real Real -> (Matrix Number))
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(define (matrix-2d-reflection a b)
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; reflection about the line through (0,0) and (a,b)
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(define a2 (* a a))
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(define b2 (* b b))
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(define 2ab (* 2 a b))
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(define norm2 (+ a2 b2))
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(define 2ab/norm2 (/ 2ab norm2))
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(matrix/dim 2 2
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(/ (- a2 b2) norm2) 2ab/norm2
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2ab/norm2 (/ (- b2 a2) norm2)))
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(: matrix-2d-orthogonal-projection : Real Real -> (Matrix Number))
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; orthogonal projection onto the line through (0,0) and (a,b)
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(define (matrix-2d-orthogonal-projection a b)
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(define a2 (* a a))
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(define b2 (* b b))
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(define ab (* a b))
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(define norm2 (+ a2 b2))
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(define ab/norm2 (/ ab norm2))
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(matrix/dim 2 2
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(/ a2 norm2) ab/norm2
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ab/norm2 (/ b2 norm2)))
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