74 lines
2.3 KiB
Factor
74 lines
2.3 KiB
Factor
! (c)2009 Joe Groff, see BSD license
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USING: accessors arrays combinators combinators.short-circuit kernel math math.vectors
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math.functions sequences ;
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IN: math.affine-transforms
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TUPLE: affine-transform { x read-only } { y read-only } { origin read-only } ;
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C: <affine-transform> affine-transform
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CONSTANT: identity-transform T{ affine-transform f { 1.0 0.0 } { 0.0 1.0 } { 0.0 0.0 } }
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: axes ( a -- a' )
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[ x>> ] [ y>> ] bi { 0.0 0.0 } <affine-transform> ;
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: a.v ( a v -- v )
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[ [ x>> ] [ first ] bi* v*n ]
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[ [ y>> ] [ second ] bi* v*n ]
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[ drop origin>> ] 2tri
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v+ v+ ;
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: <identity> ( -- a )
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{ 1.0 0.0 } { 0.0 1.0 } { 0.0 0.0 } <affine-transform> ;
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: <translation> ( origin -- a )
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[ { 1.0 0.0 } { 0.0 1.0 } ] dip <affine-transform> ;
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: <rotation> ( theta -- transform )
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[ cos ] [ sin ] bi
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[ 2array ] [ neg swap 2array ] 2bi { 0.0 0.0 } <affine-transform> ;
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: <scale> ( x y -- transform )
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[ 0.0 2array ] [ 0.0 swap 2array ] bi* { 0.0 0.0 } <affine-transform> ;
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: center-rotation ( transform center -- transform )
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[ [ x>> ] [ y>> ] [ ] tri ] dip [ vneg a.v ] [ v+ ] bi <affine-transform> ;
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: flatten-transform ( transform -- array )
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[ x>> ] [ y>> ] [ origin>> ] tri 3append ;
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: |a| ( a -- det )
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[ [ x>> first ] [ y>> second ] bi * ]
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[ [ x>> second ] [ y>> first ] bi * ] bi - ;
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: (inverted-axes) ( a -- x y )
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[ [ y>> second ] [ x>> second neg ] bi 2array ]
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[ [ y>> first neg ] [ x>> first ] bi 2array ]
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[ |a| ] tri
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[ v/n ] curry bi@ ;
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: inverse-axes ( a -- a^-1 )
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(inverted-axes) { 0.0 0.0 } <affine-transform> ;
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: inverse-transform ( a -- a^-1 )
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[ inverse-axes [ x>> ] [ y>> ] [ ] tri ] [ origin>> ] bi
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a.v vneg <affine-transform> ;
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: transpose-axes ( a -- a^T )
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[ [ x>> first ] [ y>> first ] bi 2array ]
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[ [ x>> second ] [ y>> second ] bi 2array ]
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[ origin>> ] tri <affine-transform> ;
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: a. ( a a -- a )
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{
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[ [ transpose-axes x>> ] [ x>> ] bi* v. ]
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[ [ transpose-axes y>> ] [ x>> ] bi* v. ]
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[ [ transpose-axes x>> ] [ y>> ] bi* v. ]
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[ [ transpose-axes y>> ] [ y>> ] bi* v. ]
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[ origin>> a.v ]
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} 2cleave
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[ [ 2array ] 2bi@ ] dip <affine-transform> ;
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: a~ ( a b epsilon -- ? )
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{
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[ [ [ x>> ] bi@ ] dip v~ ]
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[ [ [ y>> ] bi@ ] dip v~ ]
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[ [ [ origin>> ] bi@ ] dip v~ ]
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} 3&& ;
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