Data commit

Task/Sutherland-Hodgman-polygon-clipping/MATLAB/sutherland-hodgman-polygon-clipping-1.m

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+%The inputs are a table of x-y pairs for the verticies of the subject
+%polygon and boundary polygon. (x values in column 1 and y values in column
+%2) The output is a table of x-y pairs for the clipped version of the
+%subject polygon.
+
+function clippedPolygon = sutherlandHodgman(subjectPolygon,clipPolygon)
+
+%% Helper Functions
+
+    %computerIntersection() assumes the two lines intersect
+    function intersection = computeIntersection(line1,line2)
+
+        %this is an implementation of
+        %http://en.wikipedia.org/wiki/Line-line_intersection
+
+        intersection = zeros(1,2);
+
+        detL1 = det(line1);
+        detL2 = det(line2);
+
+        detL1x = det([line1(:,1),[1;1]]);
+        detL1y = det([line1(:,2),[1;1]]);
+
+        detL2x = det([line2(:,1),[1;1]]);
+        detL2y = det([line2(:,2),[1;1]]);
+
+        denominator = det([detL1x detL1y;detL2x detL2y]);
+
+        intersection(1) = det([detL1 detL1x;detL2 detL2x]) / denominator;
+        intersection(2) = det([detL1 detL1y;detL2 detL2y]) / denominator;
+
+    end %computeIntersection
+
+    %inside() assumes the boundary is oriented counter-clockwise
+    function in = inside(point,boundary)
+
+        pointPositionVector = [diff([point;boundary(1,:)]) 0];
+        boundaryVector = [diff(boundary) 0];
+        crossVector = cross(pointPositionVector,boundaryVector);
+
+        if ( crossVector(3) <= 0 )
+            in = true;
+        else
+            in = false;
+        end
+
+    end %inside
+
+%% Sutherland-Hodgman Algorithm
+
+    clippedPolygon = subjectPolygon;
+    numVerticies = size(clipPolygon,1);
+    clipVertexPrevious = clipPolygon(end,:);
+
+    for clipVertex = (1:numVerticies)
+
+        clipBoundary = [clipPolygon(clipVertex,:) ; clipVertexPrevious];
+
+        inputList = clippedPolygon;
+
+        clippedPolygon = [];
+        if ~isempty(inputList),
+            previousVertex = inputList(end,:);
+        end
+
+        for subjectVertex = (1:size(inputList,1))
+
+            if ( inside(inputList(subjectVertex,:),clipBoundary) )
+
+                if( not(inside(previousVertex,clipBoundary)) )
+                    subjectLineSegment = [previousVertex;inputList(subjectVertex,:)];
+                    clippedPolygon(end+1,1:2) = computeIntersection(clipBoundary,subjectLineSegment);
+                end
+
+                clippedPolygon(end+1,1:2) = inputList(subjectVertex,:);
+
+            elseif( inside(previousVertex,clipBoundary) )
+                    subjectLineSegment = [previousVertex;inputList(subjectVertex,:)];
+                    clippedPolygon(end+1,1:2) = computeIntersection(clipBoundary,subjectLineSegment);
+            end
+
+            previousVertex = inputList(subjectVertex,:);
+            clipVertexPrevious = clipPolygon(clipVertex,:);
+
+        end %for subject verticies
+    end %for boundary verticies
+end %sutherlandHodgman

Task/Sutherland-Hodgman-polygon-clipping/MATLAB/sutherland-hodgman-polygon-clipping-2.m

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+>> subject = [[50;200;350;350;250;200;150;100;100],[150;50;150;300;300;250;350;250;200]];
+>> clipPolygon = [[100;300;300;100],[100;100;300;300]];
+>> clippedSubject = sutherlandHodgman(subject,clipPolygon);
+>> plot([subject(:,1);subject(1,1)],[subject(:,2);subject(1,2)],[0,0,1])
+>> hold on
+>> plot([clipPolygon(:,1);clipPolygon(1,1)],[clipPolygon(:,2);clipPolygon(1,2)],'r')
+>> patch(clippedSubject(:,1),clippedSubject(:,2),0);
+>> axis square