コミット: 7ff29fb8f53f14a882d75b05af9a84155d2a317b - mmath (git)

Mercury Geometry and Math Library

コミットメタ情報

• リビジョン: 7ff29fb8f53f14a882d75b05af9a84155d2a317b (tree)
• 日時: 2022-04-24 05:04:00
• 作者: Emily Dioxideson <emily@eter...>
• コミッター: Emily Dioxideson

ログメッセージ

Use vectors to implement geometry2d

変更サマリ

• modified: mmath.geometry2d.m

差分

--- a/mmath.geometry2d.m
+++ b/mmath.geometry2d.m
@@ -20,30 +20,116 @@
 
 %------------------------------------------------------------------------------%
 
-:- type segment --->
-    segment(seg_x1::float, seg_y1::float, seg_x2::float, seg_y2::float).
+:- type segment ---> segment(seg_p1::vector2, seg_p2::vector2).
+
+:- func segment(float, float, float, float) = segment.
+:- mode segment(in, in, in, in) = (out) is det.
+:- mode segment(di, di, di, di) = (uo) is det.
+:- mode segment(mdi, mdi, mdi, mdi) = (muo) is det.
+:- mode segment(out, out, out, out) = (in) is det.
+:- mode segment(uo, uo, uo, uo) = (di) is det.
+:- mode segment(muo, muo, muo, muo) = (mdi) is det.
+:- mode segment(in, in, in, in) = (in) is semidet. % implied.
+
+:- func seg_x1(segment) = float.
+:- func seg_y1(segment) = float.
+:- func seg_x2(segment) = float.
+:- func seg_y2(segment) = float.
+
+:- func 'seg_x1 :='(float, segment) = segment.
+:- func 'seg_y1 :='(float, segment) = segment.
+:- func 'seg_x2 :='(float, segment) = segment.
+:- func 'seg_y2 :='(float, segment) = segment.
 
 %------------------------------------------------------------------------------%
 
-:- type rectangle --->
-    rectangle(rect_x::float, rect_y::float, rect_w::float, rect_h::float).
+:- type rectangle ---> rectangle(
+    rect_pt::vector2,
+    rect_w::float,
+    rect_h::float).
+
+:- func rectangle(float, float, float, float) = rectangle.
+:- mode rectangle(in, in, in, in) = (out) is det.
+:- mode rectangle(di, di, di, di) = (uo) is det.
+:- mode rectangle(mdi, mdi, mdi, mdi) = (muo) is det.
+:- mode rectangle(out, out, out, out) = (in) is det.
+:- mode rectangle(uo, uo, uo, uo) = (di) is det.
+:- mode rectangle(muo, muo, muo, muo) = (mdi) is det.
+:- mode rectangle(in, in, in, in) = (in) is semidet. % implied.
+
+:- func rect_x(rectangle) = float.
+:- func rect_y(rectangle) = float.
+
+:- func 'rect_x :='(float, rectangle) = rectangle.
+:- func 'rect_y :='(float, rectangle) = rectangle.
 
 %------------------------------------------------------------------------------%
 
-:- type circle --->
-    circle(circle_x::float, circle_y::float, radius::float).
+:- type circle ---> circle(circle_center::vector2, radius::float).
+
+:- func circle(float, float, float) = circle.
+:- mode circle(in, in, in) = (out) is det.
+:- mode circle(di, di, di) = (uo) is det.
+:- mode circle(mdi, mdi, mdi) = (muo) is det.
+:- mode circle(out, out, out) = (in) is det.
+:- mode circle(uo, uo, uo) = (di) is det.
+:- mode circle(muo, muo, muo) = (mdi) is det.
+:- mode circle(in, in, in) = (in) is semidet. % implied.
+
+:- func circle_x(circle) = float.
+:- func circle_y(circle) = float.
+
+:- func 'circle_x :='(float, circle) = circle.
+:- func 'circle_y :='(float, circle) = circle.
 
 %------------------------------------------------------------------------------%
 
-:- type point --->
-    point(x::float, y::float).
+:- type point == vector2.
+
+:- func point(float, float) = point.
+:- mode point(in, in) = (out) is det.
+:- mode point(di, di) = (uo) is det.
+:- mode point(mdi, mdi) = (muo) is det.
+:- mode point(out, out) = (in) is det.
+:- mode point(uo, uo) = (di) is det.
+:- mode point(muo, muo) = (mdi) is det.
+:- mode point(in, in) = (in) is semidet. % implied.
+
+:- func x(point) = float.
+:- func y(point) = float.
+
+:- func 'x :='(float, point) = point.
+:- func 'y :='(float, point) = point.
 
 %------------------------------------------------------------------------------%
 
-:- type triangle --->
-    triangle(tri_x1::float, tri_y1::float,
-        tri_x2::float, tri_y2::float,
-        tri_x3::float, tri_y3::float).
+:- type triangle ---> triangle(
+    tri_p1::vector2,
+    tri_p2::vector2,
+    tri_p3::vector2).
+
+:- func triangle(float, float, float, float, float, float) = triangle.
+:- mode triangle(in, in, in, in, in, in) = (out) is det.
+:- mode triangle(di, di, di, di, di, di) = (uo) is det.
+:- mode triangle(mdi, mdi, mdi, mdi, mdi, mdi) = (muo) is det.
+:- mode triangle(out, out, out, out, out, out) = (in) is det.
+:- mode triangle(uo, uo, uo, uo, uo, uo) = (di) is det.
+:- mode triangle(muo, muo, muo, muo, muo, muo) = (mdi) is det.
+:- mode triangle(in, in, in, in, in, in) = (in) is semidet. % implied.
+
+:- func tri_x1(triangle) = float.
+:- func tri_y1(triangle) = float.
+:- func tri_x2(triangle) = float.
+:- func tri_y2(triangle) = float.
+:- func tri_x3(triangle) = float.
+:- func tri_y3(triangle) = float.
+
+:- func 'tri_x1 :='(float, triangle) = triangle.
+:- func 'tri_y1 :='(float, triangle) = triangle.
+:- func 'tri_x2 :='(float, triangle) = triangle.
+:- func 'tri_y2 :='(float, triangle) = triangle.
+:- func 'tri_x3 :='(float, triangle) = triangle.
+:- func 'tri_y3 :='(float, triangle) = triangle.
 
 %------------------------------------------------------------------------------%
 
@@ -123,22 +209,6 @@
 
 %------------------------------------------------------------------------------%
 
-:- pred segment_endpoints(segment, point, point).
-:- mode segment_endpoints(in, out, out) is det.
-:- mode segment_endpoints(di, uo, uo) is det.
-:- mode segment_endpoints(out, in, in) is det.
-:- mode segment_endpoints(uo, di, di) is det.
-
-%------------------------------------------------------------------------------%
-
-:- pred triangle_endpoints(triangle, point, point, point).
-:- mode triangle_endpoints(in, out, out, out) is det.
-:- mode triangle_endpoints(di, uo, uo, uo) is det.
-:- mode triangle_endpoints(out, in, in, in) is det.
-:- mode triangle_endpoints(uo, di, di, di) is det.
-
-%------------------------------------------------------------------------------%
-
 :- pred triangle_segments(triangle, segment, segment, segment).
 :- mode triangle_segments(in, out, out, out) is det.
 
@@ -232,6 +302,76 @@
 
 %------------------------------------------------------------------------------%
 
+:- pragma inline(segment/4).
+segment(X1, Y1, X2, Y2) = segment(vector(X1, Y1), vector(X2, Y2)).
+
+seg_x1(segment(vector(X, _), _)) = X.
+seg_y1(segment(vector(_, Y), _)) = Y.
+seg_x2(segment(_, vector(X, _))) = X.
+seg_y2(segment(_, vector(_, Y))) = Y.
+
+'seg_x1 :='(X, segment(vector(_, Y), P2)) = segment(vector(X, Y), P2).
+'seg_y1 :='(Y, segment(vector(X, _), P2)) = segment(vector(X, Y), P2).
+'seg_x2 :='(X, segment(P1, vector(_, Y))) = segment(P1, vector(X, Y)).
+'seg_y2 :='(Y, segment(P1, vector(X, _))) = segment(P1, vector(X, Y)).
+
+%------------------------------------------------------------------------------%
+
+:- pragma inline(rectangle/4).
+rectangle(X, Y, W, H) = rectangle(vector(X, Y), W, H).
+
+rect_x(rectangle(vector(X, _), _, _)) = X.
+rect_y(rectangle(vector(_, Y), _, _)) = Y.
+
+'rect_x :='(X, rectangle(vector(_, Y), W, H)) = rectangle(vector(X, Y), W, H).
+'rect_y :='(Y, rectangle(vector(X, _), W, H)) = rectangle(vector(X, Y), W, H).
+
+%------------------------------------------------------------------------------%
+
+:- pragma inline(circle/3).
+circle(X, Y, R) = circle(vector(X, Y), R).
+
+circle_x(circle(vector(X, _), _)) = X.
+circle_y(circle(vector(_, Y), _)) = Y.
+
+'circle_x :='(X, circle(vector(_, Y), R)) = circle(vector(X, Y), R).
+'circle_y :='(Y, circle(vector(X, _), R)) = circle(vector(X, Y), R).
+
+%------------------------------------------------------------------------------%
+
+:- pragma inline(point/2).
+point(X, Y) = vector(X, Y).
+
+x(vector(X, _)) = X.
+y(vector(_, Y)) = Y.
+
+'x :='(X, vector(_, Y)) = vector(X, Y).
+'y :='(Y, vector(X, _)) = vector(X, Y).
+
+%------------------------------------------------------------------------------%
+
+:- pragma inline(triangle/6).
+triangle(X1, Y1, X2, Y2, X3, Y3) = triangle(
+    vector(X1, Y1),
+    vector(X2, Y2),
+    vector(X3, Y3)).
+
+tri_x1(triangle(vector(X, _), _, _)) = X.
+tri_y1(triangle(vector(_, Y), _, _)) = Y.
+tri_x2(triangle(_, vector(X, _), _)) = X.
+tri_y2(triangle(_, vector(_, Y), _)) = Y.
+tri_x3(triangle(_, _, vector(X, _))) = X.
+tri_y3(triangle(_, _, vector(_, Y))) = Y.
+
+'tri_x1 :='(X, triangle(vector(_, Y), P2, P3)) = triangle(vector(X, Y), P2, P3).
+'tri_y1 :='(Y, triangle(vector(X, _), P2, P3)) = triangle(vector(X, Y), P2, P3).
+'tri_x2 :='(X, triangle(P1, vector(_, Y), P3)) = triangle(P1, vector(X, Y), P3).
+'tri_y2 :='(Y, triangle(P1, vector(X, _), P3)) = triangle(P1, vector(X, Y), P3).
+'tri_x3 :='(X, triangle(P1, P2, vector(_, Y))) = triangle(P1, P2, vector(X, Y)).
+'tri_y3 :='(Y, triangle(P1, P2, vector(X, _))) = triangle(P1, P2, vector(X, Y)).
+
+%------------------------------------------------------------------------------%
+
 % is_in_range(X, M, N)
 % Unifies if X is between M and N
 :- pred is_in_range(float, float, float).
@@ -331,22 +471,10 @@ rectangle_contains(rectangle(X1, Y1, W1, H1), rectangle(X2, Y2, W2, H2)) :-
 
 %------------------------------------------------------------------------------%
 
-segment_endpoints(segment(X1, Y1, X2, Y2), point(X1, Y1), point(X2, Y2)).
-
-%------------------------------------------------------------------------------%
-
-triangle_endpoints(triangle(X1, Y1, X2, Y2, X3, Y3),
-    point(X1, Y1),
-    point(X2, Y2),
-    point(X3, Y3)).
-
-%------------------------------------------------------------------------------%
-
-triangle_segments(Triangle, S1, S2, S3) :-
-    triangle_endpoints(Triangle, P1, P2, P3),
-    segment_endpoints(S1, P1, P2),
-    segment_endpoints(S2, P2, P3),
-    segment_endpoints(S3, P3, P1).
+triangle_segments(triangle(P1, P2, P3), S1, S2, S3) :-
+    S1 = segment(P1, P2),
+    S2 = segment(P2, P3),
+    S3 = segment(P3, P1).
 
 %------------------------------------------------------------------------------%
 
@@ -481,35 +609,29 @@ collide_segments(S1, S2, Point) :-
 
 %------------------------------------------------------------------------------%
 
-collide_segment_circle(Segment, Circle, P) :-
-    segment_endpoints(Segment, Point1, Point2),
+collide_segment_circle(segment(P1, P2), Circle, P) :-
     
     % If neither of the end points are within the circle, then check if the circle's
     % center is within the radius of the segment
     ( if
-        point_inside(Circle, Point1)
+        point_inside(Circle, P1)
     then
-        P = Point1
+        P = P1
     else if
-        point_inside(Circle, Point2)
+        point_inside(Circle, P2)
     then
-        P = Point2
+        P = P2
     else
         % If we take the dot product of the center of the circle and one of the
         % endpoints on the segment, this will tell us what the nearest point on
         % the segment is to the circle.
         % We can then test this location on the line for being within the radius
         % of the center of the circle.
-        Point1 = point(X1, Y1),
-        Vector1 = vector(X1, Y1),
-        Point2 = point(X2, Y2),
-        Vector2 = vector(X2, Y2),
-        
-        Circle = geometry2d.circle(XC, YC, _),
+        Circle = geometry2d.circle(Center, _),
         
         % Adjust the center and the segment to start at Point1
-        SegmentVector = Vector2 - Vector1,
-        CenterVector = vector(XC, YC) - Vector1,
+        SegmentVector = P2 - P1,
+        CenterVector = Center - P1,
         
         % Get the length of the segment, which is our scaling value
         Length = vector.magnitude(SegmentVector),
@@ -519,26 +641,26 @@ collide_segment_circle(Segment, Circle, P) :-
         
         T >= 0.0, T =< 1.0,
         
-        SegmentVector * T = vector(NearestX, NearestY),
-        P = geometry2d.point(NearestX + X1, NearestY + Y1),
+        SegmentVector * T = Nearest,
+        P =  Nearest + P1,
         point_inside(Circle, P)
     ).
 
 %------------------------------------------------------------------------------%
 
 collide_segment_rectangle(Segment, Rect, P) :-
-    segment_endpoints(Segment, Point1, Point2),
+    Segment = segment(P1, P2), 
     
     % If neither of the end points are within the rectangle, then try to
     % intersect the segments.
     ( if
-        point_inside(Rect, Point1)
+        point_inside(Rect, P1)
     then
-        P = Point1
+        P = P1
     else if
-        point_inside(Rect, Point2)
+        point_inside(Rect, P2)
     then
-        P = Point2
+        P = P2
     else
         rectangles_intersect(Rect, bounding_box(Segment)),
         Rect = rectangle(X, Y, W, H),
@@ -547,23 +669,19 @@ collide_segment_rectangle(Segment, Rect, P) :-
         C3 = point(X + W, Y + H),
         C4 = point(X,     Y + H),
         ( if
-            segment_endpoints(RectSegment, C1, C2),
-            collide_segments(RectSegment, Segment, SemiP)
+            collide_segments(segment(C1, C2), Segment, SemiP)
         then
             P = SemiP
         else if
-            segment_endpoints(RectSegment, C2, C3),
-            collide_segments(RectSegment, Segment, SemiP)
+            collide_segments(segment(C2, C3), Segment, SemiP)
         then
             P = SemiP
         else if
-            segment_endpoints(RectSegment, C3, C4),
-            collide_segments(RectSegment, Segment, SemiP)
+            collide_segments(segment(C3, C4), Segment, SemiP)
         then
             P = SemiP
         else
-            segment_endpoints(RectSegment, C4, C1),
-            collide_segments(RectSegment, Segment, P)
+            collide_segments(segment(C4, C1), Segment, P)
         )
     ).
 
@@ -601,8 +719,8 @@ point_to_vector(geometry2d.point(X, Y)) = vector(X, Y).
         H = max(Y1, Y2) - Y),
     (point_inside(_, _) :- false),
     (translate(Translate, S1, S2) :-
-        segment_endpoints(S1, S1P1, S1P2),
-        segment_endpoints(S2, S2P1, S2P2),
+        S1 = segment(S1P1, S1P2),
+        S2 = segment(S2P1, S2P2),
         translate(Translate, S1P1, S2P1),
         translate(Translate, S1P2, S2P2)),
     (convex(segment(X1, Y1, X2, Y2), 0.0, [point(X1, Y1)|[point(X2, Y2)|[]]])),
@@ -704,21 +822,13 @@ point_to_vector(geometry2d.point(X, Y)) = vector(X, Y).
             Side2 = Side3
         )
     ),
-    (translate(Point, TriangleIn, TriangleOut) :-
-        triangle_endpoints(TriangleIn, P1in, P2in, P3in),
-        triangle_endpoints(TriangleOut, P1out, P2out, P3out),
-        translate(Point, P1in, P1out),
-        translate(Point, P2in, P2out),
-        translate(Point, P3in, P3out)
-    ),
-    (convex(Triangle, 0.0, [P1, P2, P3]) :-
-        triangle_endpoints(Triangle, P1, P2, P3)
+    (translate(P, triangle(!.P1, !.P2, !.P3), triangle(!:P1, !:P2, !:P3)) :-
+        translate(P, !P1),
+        translate(P, !P2),
+        translate(P, !P3)
     ),
-	(scale(X, Y, TriangleIn) = (TriangleOut) :-
-        triangle_endpoints(TriangleIn, P1, P2, P3),
-        triangle_endpoints(TriangleOut,
-			scale(X, Y, P1),
-			scale(X, Y, P2),
-			scale(X, Y, P3))
-	)
+    convex(triangle(P1, P2, P3), 0.0, [P1|[P2|[P3|[]]]]),
+    (scale(X, Y, triangle(P1, P2, P3)) = triangle(P * P1, P * P2, P * P3) :-
+        P = vector(X, Y))
+    
 ].