REBOL [ title: "2D transformations" Purpose: "Visualize and experiment with 2D transformation matrices" comment: "If you find a nice preset please let me know!" needs: "%simple-spin-number-style.r, %simple-pop-down-style.r" Date: 12-10-2020 Version: 0.5.1 File: %transforms-2d.r Author: "Marco Antoniazzi" eMail: [luce80 AT libero DOT it] History: [ 0.0.1 [29-07-2020 "Started"] 0.5.1 [12-10-2020 "Mature enough"] ] Category: [vid gfx] library: [ level: 'intermediate platform: 'all type: 'tool domain: [math] tested-under: [View 2.7.8.3.1] support: none license: none see-also: none ] thumbnail: https://i.postimg.cc/1XkKbL1r/transforms-2d-mini.png todo: { - grid size - combine transformations } ] ; modules ; script-version , undirize , choose_file , download , load-script-thru do decompress 64#{ eJx1VUuT3DQQvvtX9CqV4lHxiCo4uUi2gMApVEIoTmZCaeyesVlZMpK8zkDx3+nWw7OzWcoHW+rX191ftyvfuXEO9T06P1rTwHExHbSVt4vrEFof3GhON3uopLad0pAV wc+qQw/doJyv9mSxefhqRw9UUdJAZ6dZ44QmZJMm2WAAAR/qD1JANfNZKq2hhK3C4BYQ73/8/u0bAcqcSzzRCkiyEk+Q0YRFXnV2Pl9AsqRArIKtw0JgipjvFtOPbvwb S+LiPYbFGQ8Koid7pHAIswoDsAB7GE2wJD6OGncRPIlaPt3A4vQNlJLFqrC0Sa6iYrUOpMn6pgchfxeQNA6qu4OgRh3PZOlwsveYT9WAqo/fjLkbrPX4B4cssOk7oHvQ rtwt1qmNmpCxLCaQ/7baLhtw+NeCPtR8Je8QZ2mNPsvsLr+q8QjGGry9uGN8XI54T5Dw4+iDf6CQ6+3wYHX0fi3q7Wq0Vf3GN6octFy+C9O0pao46A539dFAr4JKPBtx lQZXklNhiVfo6iP1HrQ62yWQhj5oEK9zBCoHNSngxwCfH62buEdfQEWeG5idPTn0kRwpTMETbCAEh3NAzzGJrSkGA4q3ICHqxGQIGpdS9bXBIItXjgRNhk/Fj8C5vJxZ lfOpGGOdh5CJvRHxDQmIZkkER2cnWNd1Fyu6s+6UxoDJ2aluQEoyNebCRC7lUSs/gPgpvhRMhEudkLBHy8VTexMj+6t6yVVRc8V3Gl1IWsSBDMVYgmNpcFgv4no8AnsQ b+dAE6YSnSkEuhjUo3LdQOYuxk8e2U+Z2HtmcZxS9vLzaMZpmbZ5ZrqODmPkRJKYe6LkZPuFLgbs7nidRbJsp1LWqJltowFpUWoc9hVc78IkT42FVNt8k0ifzdN0BLhX eqER+YzbXDtLN+322QCOlK8Df/YBp5Kt/AZewtfQPpc/yN+oyF6+Ww567ORr2y28Mpl8z2WY5j0zdEu1gc2zbCKyKqbIe7LlVOIKJpOMN95XKlBo6l+7FYVS+9OOhgYv b8HULUE7Oe4M8vCE0QXH0/LHksqvY6Cm513DqyNFjeMY4f9zIRUQNVZnzak0/QUwLWEMLzaO0uGpgSBLoke4/ZeYw9MjLluAPn8hkaB6PmtT+1rW3cOzNriFjw8SvOxX EF/unGCto9I+btGNFSmJIYS5kfIKiSxAa5VHe+duM7k435elRqU/vk6Lu9AkTW275VuYGqn4iHfxT5K4n/6XtDuIqeoOAZ2z7gbEr48HN1n/P+mfti8qwdIgT/S7Zj+r GwN+OoYptWqfnhiO/+8tY0gavGEoJRVXTKlmCfVtYiCIV9fM+ATCTuz3W7D/AGL3BZ7NCAAA } do load load-script-thru/flash/warn/from/version %simple-pop-down-style.r %../../gui/simple 0.0.4 ; 0.3.1 do load load-script-thru/flash/warn/from/version %simple-spin-number-style.r %../../gui/simple 0.8.0 ; 0.9.0 ; debug , math opened-console?: false old-print: :print print: func [value][opened-console?: true old-print value] get-err-id: func [ value [error!] ][ value: get in disarm value 'id any [ select [ missing "missing parenthesis or bracket" no-value "a word has no value" ] value value ] ] atan2: func [; author: Steeve Antoine 2009, modified by luce80 "Angle of the vector (0,0)-(x,y) with arctangent y / x. The resulting angle is in range 0 360" x [number!] y [number!] ][ if x = 0 [x: 1e-10] ;mod add arctangent y / x pick [0 180] x > 0 360 ; 0 at east add arctangent y / x pick [90 270] x > 0 ; 0 at north ] load-math: func [; let's be more "tolerant" with the input strings text [string!] ][ text: copy text replace/all text "e+" "e£" ; avoid corner cases replace/all text "+" " + " replace/all text "e£" "e+" replace/all text "e-" "e£" replace/all text "-" " - " replace/all text "e£" "e-" replace/all text "*" " * " replace/all text "/" " / " load text ] ; presets presets: copy/deep [ "identity" ["1" "0" "0" "0" "1" "0" "0" "0" "1" 0 0 0] "move" ["1" "0" "a" "0" "1" "b" "0" "0" "1" 10 5 0] "rotate" ["cosine a" "- sine a" "0" "sine a" "cosine a" "0" "0" "0" "1" 45 0 0] "scale" ["a" "0" "0" "0" "b" "0" "0" "0" "1" 2 1.5 0] "mirror x" ["-1" "0" "0" "0" "1" "0" "0" "0" "1" 0 0 0] "mirror y" ["1" "0" "0" "0" "-1" "0" "0" "0" "1" 0 0 0] "skew" ["1" "- tangent a" "0" "tangent b" "1" "0" "0" "0" "1" 30 10 0] "roto-zoom" ["1" "- tangent a" "0" "tangent a" "1" "0" "0" "0" "1" 45 0 0] "perspective" ["1" "0" "0" "0" "1" "0" "a / 10000" "b / 10000" "1" 10 15 0] "taper x" ["d" "0" "0" "0" "1" "0" "0" "0" "1" 20 0 0 "y * a / 1000 + 1"] "skew x sine" ["1" "d" "0" "0" "1" "0" "0" "0" "1" 70 0 0 "(cosine y) * a / 100"] "cross cosine angles" ["d" "0" "0" "0" "e" "0" "0" "0" "1" 80 18 0 "(cosine (y * b / 10)) * a / 100 + 1" "(cosine (x * b / 10)) * a / 100 + 1"] "cross cosine squared" ["d" "0" "0" "0" "e" "0" "0" "0" "1" -70 18 0 "(cosine (x * b / 10)) * a / 100 + 1" "(cosine (y * b / 10)) * a / 100 + 1"] "cross cosine sides" ["d" "0" "0" "0" "e" "0" "0" "0" "1" 110 0 0 "cosine (y * a / 100)" "cosine (x * a / 100)"] "cross cosine -53" ["d" "0" "0" "0" "e" "0" "0" "0" "1" 20 -53 0 "(cosine (y * b / 10)) * a / 100 + 1" "(cosine (x * b / 10)) * a / 100 + 1"] "bend x parabola" ["cosine d * y" "- sine d * x" "0" "sine d * x" "cosine d * x" "0" "0" "0" "1" 70 0 0 "a / 100"] "bend x cardio" ["cosine d" "- sine d" "0" "sine d" "cosine d" "0" "0" "0" "1" 60 0 0 "x * a / 100"] "bend roll" ["cosine d" "0" "0" "- sine d" "0" "0" "0" "0" "1" 120 0 0 "y * a / 100"] "bulge pinch" ["e" "0" "0" "0" "e" "0" "0" "0" "1" -70 0 0 "square-root (x * x) + (y * y)" "power d / 100 a / 100"] "bulge contract" ["d" "0" "0" "0" "d" "0" "x" "y" "d" 200 0 0 "1 / tangent (a / 10000)"] "wrap circle" ["cosine d" "0" "0" "0" "cosine d" "0" "0" "0" "1" 170 0 0 "((x * x) + (y * y)) * a / 10000"] "cone x" ["cosine d" "- sine d" "0" "0" "1" "0" "0" "0" "1" 80 0 0 "x * a / 100"] "fisheye" ["e" "0" "0" "0" "e" "0" "0" "0" "1" 20 0 0 "square-root (x * x) + (y * y)" "100 * tangent (arctangent d / a) / (d + .001)"] "pinwheel" ["cosine d * x" "- sine a" "0" "sine a" "cosine d * y" "0" "0" "0" "1" 120 0 0 "a / 100"] "curve y cyl" ["d" "0" "0" "e" "1" "0" "0" "0" "1" 224 156 0 "(cosine x) * b / 100" " x * a / 10000"] "curve y parabola" ["1" "0" "0" "d" "1" "0" "0" "0" "1" 160 0 0 "x * a / 10000"] "taper x sine" ["d" "0" "0" "0" "1" "0" "0" "0" "1" -45 30 90 "(sine (y * b / 10 + c)) * a / 100 + 1"] "taper x cosine" ["d" "0" "0" "0" "1" "0" "0" "0" "1" 40 30 0 "(cosine (y * b / 10)) * a / 100 + 1"] "taper x hyp" ["d" "0" "0" "0" "1" "0" "0" "0" "1" 10 30 0 "1 / (y * a / 1000 + 1)"] "twist x cosine" ["d" "0" "0" "0" "1" "0" "0" "0" "1" 30 30 0 "cosine (y * a / 10)"] "twist sine" ["cosine d" "- sine d" "0" "sine d" "cosine d" "0" "0" "0" "1" 10 0 0 "x * x * (a / 1000)"] "twirl" ["cosine e" "- sine e" "0" "sine e" "cosine e" "0" "0" "0" "1" 120 0 0 "square-root (x * x) + (y * y)" "d * a / 100"] "whirl" ["cosine e" "- sine e" "0" "sine e" "cosine e" "0" "0" "0" "1" 30 0 0 "square-root (x * x) + (y * y)" "1 / (d + 1e-10) * a * 100"] "whirl sine" ["1" "- sine e" "0" "sine e" "1" "0" "0" "0" "1" 80 0 0 "square-root (x * x) + (y * y)" "1 / (d + 1e-10) * a * 100"] ] ; load_preset , make_preset , add_preset load_preset: func [data][ foreach face win/pane [ if face/style = 'field [set-face face any [first+ data ""]] if number? face/data [set-face face first+ data] ] update ] make_preset: func [name [string!] /local preset] [ preset: reduce [name copy []] foreach face win/pane [ if face/style = 'field [append preset/2 copy face/text] if number? face/data [append preset/2 face/data] ] preset ] add_preset: func [preset [block!]][ either find pop-down-presets/data first preset [ change find presets first preset preset ; overwrite ][ insert tail pop-down-presets/data first preset insert tail presets preset ] set-face pop-down-presets first preset ] ; make_points , load_matrix , transform squares: 10 points: copy [] make_points: func [][ clear points repeat row squares + 1 [ append/only points copy [] for col 0 - (squares / 2) (squares / 2) 1 [ append/only points/(row) reduce [col * 10 row - 1 - (squares / 2) * 10] ] ] ;probe points ] matrix: [ [field-11 field-12 field-13] [field-21 field-22 field-23] [field-31 field-32 field-33] ] M: [ [0 0 0] [0 0 0] [0 0 0] ] load_matrix: func [/local value][ repeat row 3 [ repeat col 3 [ M/(row)/(col): either error? set/any 'value try [load-math get-face get matrix/(row)/(col)] [ err: get-err-id value 0 ][ get/any 'value ] ] ] ] err: false get-M: func [row col /local value][ if error? set/any 'value try [do M/(row)/(col)] [ err: get-err-id value return 0 ] if not number? get/any 'value [ err: "not a number" return 0 ] value ] transform: func [][ a: get-face spin-a b: get-face spin-b c: get-face spin-c h3-warn/color: green h3-warn/text: "OK" h3-err/text: "" show [h3-warn h3-err] repeat row squares + 1 [ repeat col squares + 1 [ x: points/(row)/(col)/1 y: points/(row)/(col)/2 d: case [ error? set/any 'value try [do load-math get-face field-d] [err: get-err-id value 0] unset? get/any 'value [0] 'else [value] ] e: case [ error? set/any 'value try [do load-math get-face field-e] [err: get-err-id value 0] unset? get/any 'value [0] 'else [value] ] ; affine x': ((get-M 1 1) * x) + ((get-M 1 2) * y) + (get-M 1 3) y': ((get-M 2 1) * x) + ((get-M 2 2) * y) + (get-M 2 3) ; non-affine w': ((get-M 3 1) * x) + ((get-M 3 2) * y) + (max .1 get-M 3 3) + 1e-10 points/(row)/(col)/1: x' / w' points/(row)/(col)/2: y' / w' ] ] if err [ h3-warn/color: red h3-warn/text: "Error" h3-err/text: form err show [h3-warn h3-err] err: false ] ] ; draw_mesh , redraw_mesh , update mesh: copy [] draw_mesh: func [/local sqmidsize][ ; sqmidsize: squares * 10 / 2 clear mesh insert tail mesh compose [ translate (box-mesh/size / 2) ; origin pen green line -50x0 50x0 ;(sqmidsize * -1x0) (sqmidsize * 1x0) line 0x-50 0x50 box -50x-50 50x50 pen black ] repeat row squares + 1 [ if row = 2 [insert tail mesh [line-width 3 pen crimson]] if row = squares [insert tail mesh [line-width 3 pen magenta]] insert tail mesh [ line ] repeat col squares + 1 [ insert tail mesh reduce [(as-pair round points/(row)/(col)/1 round points/(row)/(col)/2)] ] if row = 2 [insert tail mesh [line-width 1 pen black]] if row = squares [insert tail mesh [line-width 1 pen black]] ] repeat col squares + 1 [ insert tail mesh [ line ] repeat row squares + 1 [ insert tail mesh reduce [(as-pair round points/(row)/(col)/1 round points/(row)/(col)/2)] ] ] insert tail mesh compose [ fill-pen gray polygon (as-pair round points/1/1/1 round points/1/1/2) (as-pair round points/1/2/1 round points/1/2/2) (as-pair round points/2/1/1 round points/2/1/2) fill-pen none ] show box-mesh ;probe mesh ] redraw_mesh: does [ make_points transform attempt [draw_mesh] ] update: does [ load_matrix redraw_mesh ] ; undo undo-list: copy [] redo-list: copy [] undo-temp: none undo-id: 0 add_to_undo-list: has [new-preset] [ new-preset: make_preset form undo-id: undo-id + 1 unless none? undo-temp [ if (second new-preset) = second undo-temp [undo-id: undo-id - 1 exit] insert/only undo-list undo-temp ] undo-temp: new-preset ] undo: does [ if empty? undo-list [exit] insert/only redo-list undo-temp undo-temp: first undo-list load_preset second take undo-list ] redo: does [ if empty? redo-list [exit] insert/only undo-list undo-temp undo-temp: first redo-list load_preset second take redo-list ] ; file load_file: func [/local file-name file-names data] [ file-names: request-file/keep if none? file-names [return none] foreach file-name file-names [ attempt [ ; avoid the case when a file doesn't exist or cannot be loaded data: load file-name if any [not string? data/1 not block? data/2 (length? data) > 2] [make error! "Wrong file"] add_preset data load_preset second data add_to_undo-list ] ] ] save_file_as: func [/local name file preset][ if any [ none? name: request-text/title "Choose a name for this new preset:" empty? name: trim name none? file: request-file/keep/only/save/file append copy name ".txt" all [exists? file not confirm "File already exists, overwrite it?"] ] [exit] preset: make_preset name ;probe preset save file preset add_preset preset ] ; gui eat_events: func [;{derived from flush_events 12-May-2007 Anton Rolls} "Allow GUI messages to be processed faster then wait." /skip events [block!] "types of events to skip. Default: [move]" /local evt ] [ events: any [events [move]] ; Remove the event-port remove find system/ports/wait-list system/view/event-port ; Clear the event port of queued events while [evt: pick system/view/event-port 1][if not find events evt/type [do evt]] ; fixed by luce80 ; Re-add the event-port to the wait-list insert system/ports/wait-list system/view/event-port ] win: layout [ do [sp: 4x4] origin sp space sp style field field "0" 70 white white edge [size: 1x1] [add_to_undo-list update] style spin spin-number 80x24 0.0 low -5000 high 5000 [attempt [redraw_mesh]] style choice-btn choice-btn 95x24 style label text -1x24 font [valign: 'middle] style lab text 16x24 bold Across btn "Open..." [load_file] btn "Save as..." [save_file_as] btn "Undo" #"^Z" [undo] btn "(R)edo" #"^R" [redo] return bar-top: bar return h3 "Result:" h3-warn: h3 "OK" 70 black green h3-err: h3 "" 300 return label "Presets:" pop-down-presets: choice-btn 180 data (extract presets 2) [ load_preset select presets value add_to_undo-list ] return guide 20x0 field-11: field "1" field-12: field field-13: field here: at return field-21: field field-22: field "1" field-23: field return field-31: field field-32: field field-33: field "1" 70 return guide 0x0 lab "a:" spin-a: spin 0.0 low -1000 high 1000 label "Input:" choice-a: choice-btn "nothing" "mouse X" "angle North CW" return lab "b:" spin-b: spin label "Input:" choice-b: choice-btn "nothing" "mouse Y" return lab "c:" spin-c: spin return lab "d:" field-d: field 218 return lab "e:" field-e: field 218 return txt bold as-is {Used formulas: ; affine (when linear) x': (M11 * x) + (M12 * y) + M13 y': (M21 * x) + (M22 * y) + M23 ; non-affine w': (M13 * x) + (M23 * y) + M33 Px: x' / w' Py: y' / w' } para [tabs: 10] at here box-mesh: box 300x300 white effect [draw mesh] feel [ engage: func [face action event /local mx my][ if find [down over away] action [ mx: event/offset/x - (box-mesh/size/x / 2) my: event/offset/y - (box-mesh/size/y / 2) if "mouse X" = get-face choice-a [set-face spin-a mx redraw_mesh] if "angle North CW" = get-face choice-a [set-face spin-a atan2 mx my redraw_mesh] if "mouse Y" = get-face choice-b [set-face spin-b my redraw_mesh] ] ] ] do [bar-top/size/x: box-mesh/offset/x + box-mesh/size/x] ] insert-event-func func [face event ] [ if event/type = 'move [eat_events] ; speedup movement by avoiding following all events event ] ; main ;print "" ; open console for debug add_to_undo-list update view win if opened-console? [halt]