138 lines
3.8 KiB
Factor
138 lines
3.8 KiB
Factor
! Copyright (C) 2005, 2010 Slava Pestov, Joe Groff.
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! See http://factorcode.org/license.txt for BSD license.
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USING: accessors arrays columns kernel locals math math.bits
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math.functions math.order math.vectors sequences
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sequences.private fry ;
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IN: math.matrices
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! Matrices
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: zero-matrix ( m n -- matrix )
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'[ _ 0 <array> ] replicate ;
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: identity-matrix ( n -- matrix )
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#! Make a nxn identity matrix.
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iota dup [ = 1 0 ? ] cartesian-map ;
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:: rotation-matrix3 ( axis theta -- matrix )
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theta cos :> c
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theta sin :> s
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axis first3 :> ( x y z )
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x sq 1.0 x sq - c * + x y * 1.0 c - * z s * - x z * 1.0 c - * y s * + 3array
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x y * 1.0 c - * z s * + y sq 1.0 y sq - c * + y z * 1.0 c - * x s * - 3array
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x z * 1.0 c - * y s * - y z * 1.0 c - * x s * + z sq 1.0 z sq - c * + 3array
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3array ;
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:: rotation-matrix4 ( axis theta -- matrix )
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theta cos :> c
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theta sin :> s
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axis first3 :> ( x y z )
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x sq 1.0 x sq - c * + x y * 1.0 c - * z s * - x z * 1.0 c - * y s * + 0 4array
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x y * 1.0 c - * z s * + y sq 1.0 y sq - c * + y z * 1.0 c - * x s * - 0 4array
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x z * 1.0 c - * y s * - y z * 1.0 c - * x s * + z sq 1.0 z sq - c * + 0 4array
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{ 0.0 0.0 0.0 1.0 } 4array ;
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:: translation-matrix4 ( offset -- matrix )
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offset first3 :> ( x y z )
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{
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{ 1.0 0.0 0.0 x }
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{ 0.0 1.0 0.0 y }
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{ 0.0 0.0 1.0 z }
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{ 0.0 0.0 0.0 1.0 }
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} ;
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: >scale-factors ( number/sequence -- x y z )
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dup number? [ dup dup ] [ first3 ] if ;
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:: scale-matrix3 ( factors -- matrix )
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factors >scale-factors :> ( x y z )
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{
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{ x 0.0 0.0 }
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{ 0.0 y 0.0 }
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{ 0.0 0.0 z }
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} ;
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:: scale-matrix4 ( factors -- matrix )
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factors >scale-factors :> ( x y z )
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{
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{ x 0.0 0.0 0.0 }
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{ 0.0 y 0.0 0.0 }
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{ 0.0 0.0 z 0.0 }
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{ 0.0 0.0 0.0 1.0 }
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} ;
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: ortho-matrix4 ( dim -- matrix )
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[ recip ] map scale-matrix4 ;
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:: frustum-matrix4 ( xy-dim near far -- matrix )
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xy-dim first2 :> ( x y )
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near x /f :> xf
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near y /f :> yf
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near far + near far - /f :> zf
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2 near far * * near far - /f :> wf
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{
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{ xf 0.0 0.0 0.0 }
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{ 0.0 yf 0.0 0.0 }
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{ 0.0 0.0 zf wf }
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{ 0.0 0.0 -1.0 0.0 }
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} ;
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:: skew-matrix4 ( theta -- matrix )
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theta tan :> zf
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{
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{ 1.0 0.0 0.0 0.0 }
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{ 0.0 1.0 0.0 0.0 }
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{ 0.0 zf 1.0 0.0 }
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{ 0.0 0.0 0.0 1.0 }
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} ;
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! Matrix operations
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: mneg ( m -- m ) [ vneg ] map ;
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: n*m ( n m -- m ) [ n*v ] with map ;
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: m*n ( m n -- m ) [ v*n ] curry map ;
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: n/m ( n m -- m ) [ n/v ] with map ;
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: m/n ( m n -- m ) [ v/n ] curry map ;
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: m+ ( m m -- m ) [ v+ ] 2map ;
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: m- ( m m -- m ) [ v- ] 2map ;
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: m* ( m m -- m ) [ v* ] 2map ;
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: m/ ( m m -- m ) [ v/ ] 2map ;
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: v.m ( v m -- v ) flip [ v. ] with map ;
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: m.v ( m v -- v ) [ v. ] curry map ;
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: m. ( m m -- m ) flip [ swap m.v ] curry map ;
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: m~ ( m m epsilon -- ? ) [ v~ ] curry 2all? ;
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: mmin ( m -- n ) [ 1/0. ] dip [ [ min ] each ] each ;
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: mmax ( m -- n ) [ -1/0. ] dip [ [ max ] each ] each ;
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: mnorm ( m -- n ) dup mmax abs m/n ;
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: cross ( vec1 vec2 -- vec3 )
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[ [ { 1 2 0 } vshuffle ] [ { 2 0 1 } vshuffle ] bi* v* ]
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[ [ { 2 0 1 } vshuffle ] [ { 1 2 0 } vshuffle ] bi* v* ] 2bi v- ; inline
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: proj ( v u -- w )
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[ [ v. ] [ norm-sq ] bi / ] keep n*v ;
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: perp ( v u -- w )
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dupd proj v- ;
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: angle-between ( v u -- a )
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[ normalize ] bi@ v. acos ;
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: (gram-schmidt) ( v seq -- newseq )
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[ dupd proj v- ] each ;
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: gram-schmidt ( seq -- orthogonal )
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V{ } clone [ over (gram-schmidt) over push ] reduce ;
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: norm-gram-schmidt ( seq -- orthonormal )
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gram-schmidt [ normalize ] map ;
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: m^n ( m n -- n )
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make-bits over first length identity-matrix
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[ [ dupd m. ] when [ dup m. ] dip ] reduce nip ;
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