DIRECTORY Imager, ImagerBox, ImagerTransformation, Geom2D, Vector2; Geom2DImpl: CEDAR PROGRAM IMPORTS Geom2D, ImagerBox, ImagerTransformation, Vector2 EXPORTS Geom2D = BEGIN OPEN Geom2D; Singularity: PUBLIC SIGNAL = CODE; id: PUBLIC Transform _ ImagerTransformation.Translate[[0, 0]]; Project: PUBLIC PROC [on, what: Vec] RETURNS [Vec] = {l2, d: Number; l2 _ on.x * on.x + on.y * on.y; IF l2 = 0 THEN SIGNAL Singularity[]; d _ on.x * what.x + on.y * what.y; RETURN [[(on.x * d)/l2, (on.y * d)/l2]]}; Displace: PUBLIC PROC [p: Vec, a: Rect] RETURNS [Rect] = {RETURN [[a.x+p.x, a.y+p.y, a.w, a.h]]}; DirectionOf: PUBLIC PROC [p: Vec] RETURNS [Direction] = {IF p.Length[] = 0 THEN SIGNAL Singularity[]; RETURN [IF p.x = 0 THEN [Y, SGN[p.y]] ELSE IF p.y = 0 THEN [X, SGN[p.x]] ELSE ERROR]}; SGN: PROC [n: Number] RETURNS [Dir] = {RETURN [IF n < 0 THEN -1 ELSE IF n > 0 THEN 1 ELSE 0]}; LineRect: PUBLIC PROC [l: Line] RETURNS [r: Rect] = { [r.x, r.w] _ MinDelt[l.from.x, l.to.x]; [r.y, r.h] _ MinDelt[l.from.y, l.to.y]}; BloatVec: PUBLIC PROC [p: Vec, by: Number] RETURNS [Rect] = {RETURN [[p.x-by, p.y-by, by*2, by*2]]}; BloatRect: PUBLIC PROC [r: Rect, by: Number] RETURNS [Rect] = {RETURN [[r.x-by, r.y-by, r.w+by*2, r.h+by*2]]}; BloatLine: PUBLIC PROC [l: Line, by: Number] RETURNS [r: Rect] = {r _ BloatRect[LineRect[l], by]}; MinMax: PROC [a, b: Number] RETURNS [min, max: Number] = {IF b < a THEN RETURN[b, a] ELSE RETURN[a, b]}; MinDelt: PROC [a, b: Number] RETURNS [min, delta: Number] = {IF b < a THEN RETURN[b, a-b] ELSE RETURN[a, b-a]}; UnitNormalToward: PUBLIC PROC [l: Line, p: Vec] RETURNS [u: Vec] = { dx, dy: Number; e: Number _ (p.x - l.from.x) * (dy _ l.to.y - l.from.y) - (dx _ l.to.x - l.from.x) * (p.y - l.from.y); IF e = 0 THEN SIGNAL Singularity[] ELSE RETURN [IF e > 0 THEN Vector2.Unit[[dy, -dx]] ELSE IF e < 0 THEN Vector2.Unit[[-dy, dx]] ELSE ERROR]; }; Parallel: PUBLIC PROC [a, b: Vec] RETURNS [BOOLEAN] = {RETURN [a.x * b.y - a.y * b.x = 0]}; In: PUBLIC PROC [p: Vec, r: Rect] RETURNS [BOOLEAN] = {RETURN [p.x >= r.x AND p.x <= r.x+r.w AND p.y >= r.y AND p.y <= r.y+r.h]}; SweepRects: PUBLIC PROC [a, b: Rect] RETURNS [Rect] = {RETURN [[a.x+b.x, a.y+b.y, a.w+b.w, a.h+b.h]]}; UpdateRects: PUBLIC PROC [a, b: Rect] RETURNS [Rect] = { ab: ImagerBox.Box _ ImagerBox.BoxFromRectangle[a]; bb: ImagerBox.Box _ ImagerBox.BoxFromRectangle[b]; RETURN [ImagerBox.RectangleFromBox[[ MIN[ab.xmin, bb.xmin], MIN[ab.ymin, bb.ymin], MAX[ab.xmax, bb.xmax], MAX[ab.ymax, bb.ymax] ]]]}; UpdateFRect: PUBLIC PROC [a: Rect, f: FRect] RETURNS [FRect] = {RETURN [[TRUE, IF f.defined THEN UpdateRects[a, f.r] ELSE a]]}; ExtremaOfRect: PUBLIC PROC [r: Rect, n: Vec] RETURNS [min, max: Vec] = { b: ImagerBox.Box _ ImagerBox.BoxFromRectangle[r]; e: ExtremaRec _ Extreme[n, [b.xmin, b.ymin], Extreme[n, [b.xmin, b.ymax], Extreme[n, [b.xmax, b.ymin], StartExtreme[n, [b.xmax, b.ymax]]]]]; RETURN [e.minV, e.maxV]}; RotateBy90s: PUBLIC PROC [t: Transform, i: INTEGER] RETURNS [Transform] = {RETURN [SELECT ((i MOD 4) + 4) MOD 4 FROM 0 => t, 2 => t.PostScale[-1], 1 => t.Concat[rotLeft], 3 => t.Concat[rotRight], ENDCASE => ERROR]}; rotLeft: Transform _ ImagerTransformation.Create[0, -1, 0, 1, 0, 0]; rotRight: Transform _ ImagerTransformation.Create[0, 1, 0, -1, 0, 0]; MapVecs: PUBLIC PROC [t: Transform, l: VecList] RETURNS [n: VecList] = {prev: VecList _ n _ NIL; FOR l _ l, l.rest WHILE l # NIL DO cur: VecList _ LIST[t.Transform[l.first]]; IF prev = NIL THEN n _ cur ELSE prev.rest _ cur; prev _ cur; ENDLOOP}; MapRects: PUBLIC PROC [t: Transform, l: RectList] RETURNS [n: RectList] = BEGIN prev: RectList _ n _ NIL; FOR l _ l, l.rest WHILE l # NIL DO cur: RectList _ LIST[t.TransformRectangle[l.first]]; IF prev = NIL THEN n _ cur ELSE prev.rest _ cur; prev _ cur; ENDLOOP; END; END. ░Geom2DImpl.Mesa Last Edited by: Spreitzer, June 9, 1985 1:04:00 pm PDT Mike Spreitzer January 23, 1987 2:49:49 pm PST some two dimensional geometry, with real numbers Э╩zШJЪЬЩЩ6IcodeЩ.ЧKЩJЪЬ0Щ0KЩЪ╧k Ь:ШCKШЧЪ╨bx ЬЭЬЭШKЪЭЬ1Ш8KЪЭЬ ШKШЧKЪЭЬЭЬШKШKЪЬ ЭЬЭЬЭЬШ"KЪЬЭЬ4Ш>KШЪ╧nЬЭЬЭЬЭЬШ4KШKШKЪЭЬЭЬЭЬШ$KШ"KЪЭЬ#Ш)KШЧЪЯЬЭЬЭЬЭЬ Ш8KЪЬЭЬ!Ш(KШЧЪЯЬЭЬЭЬ ЭЬШ7KЪЬЭЬЭЬЭЬШ-Ъ ЭЬЭЬ ЭЬЭЬЭЬШ%KЪ ЭЬЭЬ ЭЬЭЬЭЬШ"KЪЭЬЭЬШ KШЧЧЪЭЬЭЬ ЭЬШ%KЪЬЭЬЭЬЭЬЭЬЭЬЭЬЭЬШ8ЧKШЪЯЬЭЬЭЬЭЬШ5KШ'KШ(ЧKШЪЯЬЭЬЭЬЭЬ Ш;KЪЬЭЬ!Ш(KШЧЪЯ ЬЭЬЭЬЭЬ Ш=KЪЬЭЬ)Ш0KШЧЪЯ ЬЭЬЭЬЭЬШ@KШ!KШЧЪЯЬЭЬЭЬШ8KЪЬЭЬЭЬЭЬЭЬЭЬШ/KШЧЪЯЬЭЬЭЬШ;KЪЬЭЬЭЬЭЬ ЭЬЭЬ Ш3KШЧЪЯЬЭЬЭЬЭЬ ШDKШШ9KШ,ЧKЪЭЬЭЬЭЬШ"ЪЭЬЭЬЭЬЭЬШ2KЪЭЬЭЬЭЬШ*KЪЭЬЭЬШЧЪЬШKШЧЧЪ ЯЬЭЬЭЬ ЭЬЭЬШ5KЪЬЭЬШ%KШЧЪ ЯЬЭЬЭЬЭЬЭЬШ5KЪ ЬЭЬ ЭЬЭЬЭЬШKЧKШЪЯ ЬЭЬЭЬЭЬ Ш5KЪЬЭЬ)Ш0ЧKШЪЯЬЭЬЭЬЭЬШ8KЪЬ2Ш2KЪЬ2Ш2ЪЭЬШ$KЪЭЬЭЬШ-KЪЭЬЭЬШ,KЪЬШKШЧЧЪЯЬЭЬЭЬЭЬ Ш>KЪЬЭЬЭЬЭЬЭЬЭЬШ@KШЧЪЯ ЬЭЬЭЬШHKЪЬ1Ш1Ш,KШKШKШ%ЧKЪЭЬШЧKШЪ ЯЬЭЬЭЬЭЬЭЬШIЪ ЬЭЬЭЬЭЬ ЭЬЭШ*KШKЪЬШKШKШKЪЭЬЭЬШЧЧKШKШDKШEKШЪЯЬЭЬЭЬЭЬШFKЪЬЭЬШЪЭЬЭЬЭЬЭШ"KЪЬЭЬШ*KЪЭЬЭЬЭЬШKЪЭЬШKШKЪЭЬШ KШЧЧЪЯЬЭЬЭЬЭЬШIKЪЭШKЪЬЭЬШЪЭЬЭЬЭЬЭШ"KЪЬЭЬ Ш4KЪЭЬЭЬЭЬШKЪЭЬШKШKЪЭЬШЧKЪЭЬШЧKШKЪЭЬШKШЧЕЧш