f5fa93572d
* Gram-Schmidt using vector type * QR decomposition * Operator 1-norm and maximum norm; stub for 2-norm and angle between subspaces (`matrix-basis-angle') * `matrix-absolute-error' and `matrix-relative-error'; also predicates based on them, such as `matrix-identity?' * Lots of shuffling code about * Types that can have contracts, and an exhaustive test to make sure every value exported by `math/matrix' has a contract when used in untyped code * Some more tests (still needs some)
60 lines
1.7 KiB
Racket
60 lines
1.7 KiB
Racket
#lang typed/racket/base
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(require "matrix-types.rkt"
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"matrix-syntax.rkt")
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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 Real))
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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 [[cosθ (- sinθ)]
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[sinθ cosθ]]))
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(: matrix-2d-scaling : Real Real -> (Matrix Real))
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(define (matrix-2d-scaling sx sy)
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(matrix [[sx 0]
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[0 sy]]))
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(: matrix-2d-shear-x : Real -> (Matrix Real))
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(define (matrix-2d-shear-x k)
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(matrix [[1 k]
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[0 1]]))
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(: matrix-2d-shear-y : Real -> (Matrix Real))
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(define (matrix-2d-shear-y k)
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(matrix [[1 0]
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[k 1]]))
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(: matrix-2d-reflection : Real Real -> (Matrix Real))
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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 [[(/ (- 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 Real))
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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 [[(/ a2 norm2) ab/norm2]
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[ab/norm2 (/ b2 norm2)]]))
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