Geomatplot

Geomatplot is a Matlab interactive plot library similar to Geogebra.

Main features

1. Easy to use interactive geometry library for Matlab
2. Efficient update through the dependency graph
3. User defined callback functions for programming

Requires

1. Image Processing Toolbox
2. Mapping Toolbox (for intersection)

Geogebra-like example

clf; g = Geomatplot; ylim([-0.2 0.6]); xlim([-.1 1.1]);
A = Point([0.0 0.0]);     % draggable point, automatically labelled A
B = Point([1.0 0.0]);     % automatic labels are applied if no label is given
C = Point([.6 .55]);
ab = Segment(A,B,'b',2);  % a blue segment from A and B
bc = Segment(B,C,'b',2);  %         with LineWidth of 2
cd = Segment(C,A,'b',2);

Segment(A,Midpoint(B,C),'--');
Segment(B,Midpoint(C,A),'--');
Segment(C,Midpoint(A,B),'--');
S=Midpoint('S',A,B,C,'k',7); % Barycenter of the triangle labelled S

PerpendicularBisector(A,B,':');
PerpendicularBisector(B,C,':');
PerpendicularBisector(C,A,':');
[~,K] = Circle(A,B,C,'m--'); % Magenta dashed circumcircle of the triangle

la = AngleBisector(A,B,C,':');
lb = AngleBisector(B,C,A,':');
lc = AngleBisector(C,A,B,':');
Circle(Intersect('O',la,lb),ab,'c'); % (inscribed) circle touching segment AB

ma = PerpendicularLine(A,B,C,':');
mb = PerpendicularLine(B,C,A,':');
mc = PerpendicularLine(C,A,B,':');
M = Intersect('M',ma,mb);
Segment(M,K,'r');

2D sphere trace visualization

clf; g = Geomatplot; xlim([-1.5 1.3]); ylim([0 1.7]); disp Polygon

% You can move, create, delete vertices of the following polygon:
f = Polygon([-1 0;1 0;1 1;0.7 0.7;0.3 0.5;0 0.9;-0.5 0.3;-1 0.3],'b');

p0 = Point('p0',[-.8,1.0 ],'r');
q0 = Point('q0',[.5 ,1.05],'r',5);
v0 = (q0-p0)/Distance(p0,q0); % Operators: point-point=vector, vector/scalar = vector
Ray(p0,q0,'r',1.5);

p = p0; n=10; % Sphere tracing illustration:
for i = 1:n
    d = Distance(p,f); % distance to polygon yields a dependent scalar value
    Circle(p,d,'Color',[i/n 1-i/n 0]);
    p = p + v0*d;      % vector*scalar=vector, point+vector=point
end

Parametric curve and 2D function visualization

clf; g = Geomatplot; disp Image
b0 = Point('b0',[0.1 0.2],'r'); % draggable control points
b1 = Point('b1',[0.7 0.9],'r'); % with given labels
b2 = Point('b2',[0.9 0.2],'r');
c1 = Point('c1',[-.5 0],'k','MarkerSize',5); % adjustable corner
c2 = Point('c2',[1.5 1],'k','MarkerSize',5); %   for the image

% parametric callback with t in [0,1] and dependent variables:
bt = @(t,b0,b1,b2)  b0.*(1-t).^2 + 2*b1.*t.*(1-t) + b2.*t.^2;
b = Curve(b0,b1,b2,bt,'r',2); % A red quadratic Bézier curve

Image(b0,b1,b2,@dist2bezier,c1,c2); colorbar;
% where 'dist2bezier' is a (x,y,b0,b1,b2) -> real function

P = Point('P',[.5 .4],'y');
Circle(P,b,'y');

Query data (WIP)

From the previous example, disp(g) produces the output below. Dependent objects (they start with a 'd') measure their own callback excecution time, while the movable points measure the time to execute all objects that depend on it. While dragging, render resolutions are lowered to increase responsiveness.

>> disp(g)
Geomatplot with 6 movable and 4 dependent plots:
   label : type    runtime    mean pos   |   labels : callback                                         
    'b0' : mpoint  258.03ms [0.08 0.21]  |          :                                                  
    'b1' : mpoint  248.32ms [0.64 0.91]  |          :                                                  
    'b2' : mpoint  256.81ms [0.94 0.18]  |          :                                                  
    'c1' : mpoint  234.01ms [-0.50 0.00] |          :                                                  
    'c2' : mpoint  234.47ms [1.48 0.99]  |          :                                                  
     'P' : mpoint   0.54ms  [0.51 0.40]  |          :                                                  
'curve1' : dcurve   0.43ms  [0.55 0.43]  | b0,b1,b2 : Curve/internalcallback                           
'image1' : dimage  234.01ms [0.49 0.49]  | b0,b1,b2 : Image/internalcallback                           
     'b' : dscalar  0.24ms     [0.14     | P,curve1 : dist_point2polyline                              
     'a' : dcircle  0.30ms  [0.51 0.40]  |      P,b : @(t,c,r)c.value+r.value*[cos(2*pi*t),sin(2*pi*t)]
  Methods, Events, Superclasses

Further examples

The examples/bez.m produces the following:

Design principles

1. Common geometry should be easy to define
2. Responsive interaction, fast callbacks
3. User callbacks for advanced programmable applets

Credits

Geomatplot is developed by Csaba Bálint and Róbert Bán at Eötvös Loránd University, Budapest, Hungary.