Added file to plot a Bezier curve and an example script

BezierExample.m

@@ -0,0 +1,95 @@
+% Bezier example
+
+% This goes in a file named BezierExample.m
+
+close all
+clear all
+
+x_nodes = [];
+y_nodes = [];
+
+% Initialize figure window
+
+figure
+hold on
+xlim([0 1])
+ylim([0 1])
+
+% Collect nodes
+
+disp('Click several points on curve. Hit enter to exit')
+index = 1;
+while(true)    
+    [x,y,button] = ginput(1);
+    
+    if (isempty(x))
+        break
+    end
+    
+    if (button ~= 1)
+        continue
+    end
+    
+    % Add the new point and plot the new line segment
+    
+    x_nodes(index) = x(1);
+    y_nodes(index) = y(1);
+    if (index > 1)
+        plot(x_nodes(index-1:index),y_nodes(index-1:index))
+    end
+    
+    index = index + 1;
+end
+
+% Points have been entered. Build the collection of nodes and control
+% points that define the curve
+
+number_curves = length(x_nodes) - 1;
+bezier_points = cell(number_curves,4);
+for k = 1:number_curves
+
+    % Insert the nodes
+    
+    bezier_points{k,1} = [x_nodes(k) y_nodes(k)];
+    bezier_points{k,4} = [x_nodes(k+1) y_nodes(k+1)];
+    
+    % Create the control points
+    
+    if (k == 1)
+        bezier_points{k,2} = [x_nodes(1) y_nodes(1)] + ([x_nodes(2) y_nodes(2)] - [x_nodes(1) y_nodes(1)])/3;
+    else
+        
+        % Compute positions for control points. Arbitrarily, they will be
+        % collinear with the node in between and 1/3 of the way to the next
+        % node
+        
+        vector_1 = [x_nodes(k) y_nodes(k)] - [x_nodes(k-1) y_nodes(k-1)];
+        length_1 = norm(vector_1);
+        vector_1 = vector_1/length_1;
+        
+        vector_2 = [x_nodes(k) y_nodes(k)] - [x_nodes(k+1) y_nodes(k+1)];
+        length_2 = norm(vector_2);
+        vector_2 = vector_2/length_2;
+        
+        vector_sum = vector_1 + vector_2;
+        n = vector_sum/norm(vector_sum);
+        
+        % If vector_1 X vector_2 is negative, reverse the direction of n
+        
+        if ((vector_1(1)*vector_2(2) - vector_2(1)*vector_1(2)) < 0)
+            n = -n;
+        end
+        n_p = [-n(2) n(1)];
+        
+        bezier_points{k-1,3} = [x_nodes(k) y_nodes(k)] + n_p*length_1/3;
+        bezier_points{k,2} = [x_nodes(k) y_nodes(k)] - n_p*length_2/3;
+        
+        if (k == (number_curves))
+            
+            bezier_points{k,3} = [x_nodes(number_curves+1) y_nodes(number_curves+1)] + ...
+                                 ([x_nodes(number_curves) y_nodes(number_curves)] - [x_nodes(number_curves+1) y_nodes(number_curves+1)])/3;
+        end
+    end 
+end
+
+PlotBezier(bezier_points)

PlotBezier.m

@@ -0,0 +1,184 @@
+function PlotBezier( bezier_points )
+% Display the Bezier curve
+
+% This goes in a file named PlotBezier.m
+
+% Clear the children of the current axes
+
+cla 
+
+% Define the array of parametervectors as a column vector, so calculation
+% of points on the Bezier curve can be done in one statement
+
+t = (0:0.05:1)';
+
+number_segments = size(bezier_points,1);
+for k = 1:number_segments
+    P0 = bezier_points{k,1};
+    P1 = bezier_points{k,2};
+    P2 = bezier_points{k,3};
+    P3 = bezier_points{k,4};
+    
+    % Compute the points on this curve segment and plot them
+    
+    bezier = ((1 - t).^3)*P0 + (3*t.*(1 - t).^2)*P1 + (3*t.^2.*(1 - t))*P2 + t.^3*P3;
+    plot(bezier(:,1),bezier(:,2))
+    hold on
+    
+    % Plot dotted lines first so they will be behind the nodes and control
+    % points and thus not intercept the clicks on the nodes and control
+    % points
+    
+    plot([P0(1) P1(1)],[P0(2) P1(2)],':')
+    plot([P2(1) P3(1)],[P2(2) P3(2)],':')
+    
+    % Plot the nodes and control points
+    
+    plot(P0(1),P0(2),'o','MarkerFaceColor','k','ButtonDownFcn',@ClickMarker)
+     
+    plot(P1(1),P1(2),'o','ButtonDownFcn',@ClickMarker)
+    plot(P2(1),P2(2),'o','ButtonDownFcn',@ClickMarker)
+end
+
+% Plot the last node
+
+plot(P3(1),P3(2),'o','MarkerFaceColor','k','ButtonDownFcn',@ClickMarker)
+
+% Set the limits
+
+xlim([0 1])
+ylim([0 1])
+function ClickMarker(source,event)
+    set(ancestor(source,'figure'),'WindowButtonMotionFcn',{@DragMarker,source})
+    set(ancestor(source,'figure'),'WindowButtonupFcn',@StopDragging)
+end
+
+function DragMarker(figure,event,source)
+
+% Get current axes and coordinates of the screen point 
+
+h1=gca;
+coordinates=get(h1,'currentpoint');
+coordinates = coordinates(1,1:2);
+
+% Find the closest node or control point. This code is simplistic in the
+% sense that it always takes the nearest node or control point. If a node
+% or control point is dragged near another node or control point, then the
+% other one will be moved.
+
+segment_index = -1;
+node_control_index = -1;
+distance = Inf;
+for m = 1:size(bezier_points,1)
+    for n = 1:4
+        if (isinf(distance))
+            distance = norm(bezier_points{m,n}-coordinates);
+            segment_index = m;
+            node_control_index = n;
+        else
+            new_distance = norm(bezier_points{m,n}-coordinates);
+            if (new_distance < distance)
+                distance = new_distance;
+                segment_index = m;
+                node_control_index = n;
+            end
+        end
+    end
+end
+
+% Modify the nodes and control points
+
+old_point = bezier_points{segment_index,node_control_index};
+bezier_points{segment_index,node_control_index} = coordinates;
+
+% For an intermediate node, the coodinates are stored twice. Update the 
+% other copy
+
+if (segment_index < number_segments && node_control_index == 4)
+    bezier_points{segment_index+1,1} = coordinates;
+end
+
+if (1 < segment_index && node_control_index == 1)
+    bezier_points{segment_index-1,4} = coordinates;
+end
+
+% Moving a node or control point causes movement of other control points.
+% If a node is moved, the control points on either side need to be moved. If a
+% control point is moved, its partner acros the node must be moved
+
+if (node_control_index == 1 || node_control_index == 4)
+    
+    % Node was moved. Move attached control points
+    
+    translation_vector = bezier_points{segment_index,node_control_index} - old_point;
+    
+    if (segment_index == 1 && node_control_index == 1)
+        bezier_points{segment_index,2} = bezier_points{segment_index,2} + translation_vector;
+    elseif (segment_index == number_segments && node_control_index == 4)
+        bezier_points{segment_index,3} = bezier_points{segment_index,3} + translation_vector;
+    else
+        if (node_control_index == 1)
+            bezier_points{segment_index,2} = bezier_points{segment_index,2} + translation_vector;
+            bezier_points{segment_index-1,3} = bezier_points{segment_index-1,3} + translation_vector;
+        else
+            bezier_points{segment_index+1,2} = bezier_points{segment_index+1,2} + translation_vector;
+            bezier_points{segment_index,3} = bezier_points{segment_index,3} + translation_vector;
+        end
+    end
+else
+    
+    % Control point was moved. Rotate its partner
+    
+    if ((segment_index == 1 && node_control_index == 2) || (segment_index == number_segments && node_control_index == 3))
+        
+        % No partner. Nothing else to do
+        
+    else
+        new_point = bezier_points{segment_index,node_control_index};
+        if (node_control_index == 2)
+            
+            % Rotate previous control point
+            
+            rotation_center = bezier_points{segment_index,1};
+            other_control_point = bezier_points{segment_index-1,3};
+        else
+            
+            % Rotate next control point
+            
+            rotation_center = bezier_points{segment_index,4};
+            other_control_point = bezier_points{segment_index+1,2};
+        end
+        
+        new_vector = new_point - rotation_center;
+        new_vector = new_vector/norm(new_vector);
+        old_vector = old_point - rotation_center;
+        old_vector = old_vector/norm(old_vector);
+
+        cos_theta = sum(old_vector.*new_vector);
+        sin_theta = old_vector(1)*new_vector(2) - new_vector(1)*old_vector(2);
+        rotation_matrix = [cos_theta -sin_theta;sin_theta cos_theta];
+
+        other_control_point = other_control_point - rotation_center;
+
+        rotated_other_control_point = (rotation_matrix*(other_control_point'))' + rotation_center;
+        
+        if (node_control_index == 2)
+            bezier_points{segment_index-1,3} = rotated_other_control_point;
+        else
+            bezier_points{segment_index+1,2} = rotated_other_control_point;
+        end
+       
+    end
+end
+
+% Plot the updated curve
+
+PlotBezier(bezier_points);
+
+end
+function StopDragging(figure,event)
+    set(figure,'WindowButtonMotionFcn','')
+    set(figure,'WindowButtonUpFcn','')
+end
+
+end