--- /dev/null
+Erik Charlebois
--- /dev/null
+! Copyright (C) 2010 Erik Charlebois.
+! See http://factorcode.org/license.txt for BSD license.
+USING: help.markup help.syntax math ;
+IN: math.splines
+
+HELP: <bezier-curve>
+{ $values
+ { "control-points" "sequence of control points same dimension" }
+ { "polynomials" "sequence of polynomials for each dimension" }
+}
+{ $description "Creates bezier curve polynomials for the given control points." } ;
+
+HELP: <catmull-rom-spline>
+{ $values
+ { "points" "points on the spline" } { "m0" "initial tangent vector" } { "mn" "final tangent vector" }
+ { "polynomials-sequence" "sequence of sequences of polynomials" }
+}
+{ $description "Creates a sequence of cubic hermite curves (each a sequence of polynomials) passing through the given points and generating tangents for C1 continuity." } ;
+
+HELP: <cubic-hermite-curve>
+{ $values
+ { "p0" "start point" } { "m0" "start tangent" } { "p1" "end point" } { "m1" "end tangent" }
+ { "polynomials" "sequence of polynomials" }
+}
+{ $description "Creates a sequence of polynomials (one per dimension) for the curve passing through " { $emphasis "p0" } " and " { $emphasis "p1" } "." } ;
+
+HELP: <cubic-hermite-spline>
+{ $values
+ { "point-tangent-pairs" "sequence of point and tangent pairs" }
+ { "polynomials-sequence" "sequence of sequences of polynomials" }
+}
+{ $description "Creates a sequence of cubic hermite curves (each a sequence of polynomials) passing through the given points with the given tangents." } ;
+
+HELP: <kochanek-bartels-curve>
+{ $values
+ { "points" "points on the spline" } { "m0" "start tangent" } { "mn" "end tangent" } { "tension" number } { "bias" number } { "continuity" number }
+ { "polynomials-sequence" "sequence of sequence of polynomials" }
+}
+{ $description "Creates a sequence of cubic hermite curves (each a sequence of polynomials) passing through the given points, generating tangents with the given tuning parameters." } ;
+
+ARTICLE: "math.splines" "Common parametric curves."
+"The curve creating functions create sequences of polynomials, one for each degree of the input points. The spline creating functions create sequences of these curve polynomial sequences. The " { $vocab-link "math.splines.viewer" } " vocabulary provides a gadget to evaluate the generated polynomials and view the results.";
+
+ABOUT: "math.splines"
--- /dev/null
+! Copyright (C) 2010 Erik Charlebois
+! See http://factorcode.org/license.txt for BSD license.
+USING: accessors combinators kernel locals math math.combinatorics
+math.polynomials opengl.gl sequences ui.gadgets ui.gadgets.panes
+ui.render arrays grouping math.vectors assocs
+ui.gestures ;
+IN: math.splines
+
+<PRIVATE
+:: bernstein-polynomial-ith ( n i -- p )
+ n i nCk { 0 1 } i p^ { 1 -1 } n i - p^ p* n*p ;
+
+:: hermite-polynomial ( p0 m0 p1 m1 -- poly )
+ p0
+ m0
+ -3 p0 * -2 m0 * + 3 p1 * + m1 neg +
+ 2 p0 * m0 + -2 p1 * + m1 +
+ 4array ;
+
+:: kochanek-bartels-coefficients ( tension bias continuity -- s1 d1 s2 d2 )
+ 1 tension -
+ [
+ 1 bias +
+ [ 1 continuity + * * 2 / ]
+ [ 1 continuity - * * 2 / ] 2bi
+ ]
+ [
+ 1 bias -
+ [ 1 continuity - * * 2 / ]
+ [ 1 continuity + * * 2 / ] 2bi
+ ] bi ;
+
+:: kochanek-bartels-tangents ( points m0 mn c1 c2 -- tangents )
+ points 3 clump [
+ first3 :> ( pi-1 pi pi+1 )
+ pi pi-1 v- c1 v*n
+ pi+1 pi v- c2 v*n v+
+ ] map
+ m0 prefix
+ mn suffix ;
+PRIVATE>
+
+:: <bezier-curve> ( control-points -- polynomials )
+ control-points
+ [ length 1 - ]
+ [ first length [ { 0 } ] replicate ]
+ bi :> ( n acc )
+
+ control-points [| pt i |
+ n i bernstein-polynomial-ith :> poly
+ pt [| v j |
+ j acc [ v poly n*p p+ ] change-nth
+ ] each-index
+ ] each-index
+ acc ;
+
+:: <cubic-hermite-curve> ( p0 m0 p1 m1 -- polynomials )
+ p0 length iota [
+ {
+ [ p0 nth ] [ m0 nth ]
+ [ p1 nth ] [ m1 nth ]
+ } cleave
+ hermite-polynomial
+ ] map ;
+
+<PRIVATE
+: (cubic-hermite-spline) ( point-in-out-triplets -- polynomials-sequence )
+ 2 clump [
+ first2 [ first2 ] [ [ first ] [ third ] bi ] bi* <cubic-hermite-curve>
+ ] map ;
+PRIVATE>
+
+: <cubic-hermite-spline> ( point-tangent-pairs -- polynomials-sequence )
+ 2 clump [ first2 [ first2 ] bi@ <cubic-hermite-curve> ] map ;
+
+:: <kochanek-bartels-curve> ( points m0 mn tension bias continuity -- polynomials-sequence )
+ tension bias continuity kochanek-bartels-coefficients :> ( s1 d1 s2 d2 )
+ points m0 mn
+ [ s1 s2 kochanek-bartels-tangents ]
+ [ d1 d2 kochanek-bartels-tangents ] 3bi :> ( in out )
+ points in out [ 3array ] 3map (cubic-hermite-spline) ;
+
+: <catmull-rom-spline> ( points m0 mn -- polynomials-sequence )
+ 0 0 0 <kochanek-bartels-curve> ;
--- /dev/null
+Common parametric curves
--- /dev/null
+Erik Charlebois
\ No newline at end of file
--- /dev/null
+! Copyright (C) 2010 Erik Charlebois.
+! See http://factorcode.org/license.txt for BSD license.
+USING: locals math.splines math.splines.viewer arrays ;
+IN: math.splines.testing
+
+: test1 ( -- )
+ {
+ { { 0 0 } { 0 200 } }
+ { { 100 50 } { 0 -200 } }
+ { { 300 300 } { 500 200 } }
+ { { 400 400 } { 300 0 } }
+ } <cubic-hermite-spline> { 50 100 } 4 spline. ;
+
+: test2 ( -- )
+ {
+ { 50 50 }
+ { 100 100 }
+ { 300 200 }
+ { 350 0 }
+ { 400 400 }
+ } { 0 100 } { 100 0 } <catmull-rom-spline> { 100 50 } 50 spline. ;
+
+:: test3 ( x y z -- )
+ {
+ { 100 50 }
+ { 200 350 }
+ { 300 50 }
+ } { 0 100 } { 0 -100 } x y z <kochanek-bartels-curve> { 50 50 } 1000 spline. ;
+
+: test4 ( -- )
+ {
+ { 0 5 }
+ { 0.5 3 }
+ { 10 10 }
+ { 12 4 }
+ { 15 5 }
+ } <bezier-curve> 1array { 100 100 } 100 spline. ;
+
+: test-splines ( -- )
+ test1 test2
+ 1 0 0 test3
+ -1 0 0 test3
+ 0 1 0 test3
+ 0 -1 0 test3
+ 0 0 1 test3
+ 0 0 -1 test3
+ test4 ;
+
+
--- /dev/null
+Erik Charlebois
\ No newline at end of file
--- /dev/null
+! Copyright (C) 2010 Erik Charlebois.
+! See http://factorcode.org/license.txt for BSD license.
+USING: accessors kernel locals math math.order math.polynomials
+math.splines opengl.gl sequences ui.gadgets ui.gadgets.panes ui.render
+arrays ;
+IN: math.splines.viewer
+
+<PRIVATE
+: eval-polynomials ( polynomials-seq n -- xy-sequence )
+ [
+ [ 1 + iota ] keep [
+ /f swap [ polyval ] with map
+ ] curry with map
+ ] curry map concat ;
+PRIVATE>
+
+TUPLE: spline-gadget < gadget polynomials steps spline-dim ;
+
+M: spline-gadget pref-dim* spline-dim>> ;
+
+M:: spline-gadget draw-gadget* ( gadget -- )
+ 0 0 0 glColor3f
+
+ gadget [ polynomials>> ] [ steps>> ] bi eval-polynomials :> pts
+
+ pts [ first ] [ max ] map-reduce :> x-max
+ pts [ first ] [ min ] map-reduce :> x-min
+ pts [ second ] [ max ] map-reduce :> y-max
+ pts [ second ] [ min ] map-reduce :> y-min
+
+ pts [
+ [ first x-min - x-max x-min - / gadget spline-dim>> first * ]
+ [ second y-min - y-max y-min - / gadget spline-dim>> second * ] bi 2array
+ ] map :> pts
+
+ GL_LINE_STRIP glBegin
+ pts [
+ first2 neg gadget spline-dim>> second + glVertex2f
+ ] each
+ glEnd ;
+
+:: <spline-gadget> ( polynomials dim steps -- gadget )
+ spline-gadget new
+ dim >>spline-dim
+ polynomials >>polynomials
+ steps >>steps ;
+
+: spline. ( curve dim steps -- )
+ <spline-gadget> gadget. ;
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