Geomatplot is a Matlab interactive plot library similar to Geogebra. We showcased the library at the CAD'24 conference, see in Citation.
- Easy to use interactive geometry library for Matlab
- Efficient update through the dependency graph
- User defined callback functions for programming
- Image Processing Toolbox
- Mapping Toolbox (only for some intersections)
- Parallel Computing Toolbox (only for faster Image rendering)
clf; disp Triangle
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([0.6 .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
Text(K,"K") % add text at position
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') % Euler line
ylim([-0.2 0.6]); xlim([-.1 1.1])
clf; disp 'Sphere Trace'
% 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]);
p0 = Point('p0',[-.8,1.05],'r'); % ray start
q0 = Point('q0',[.5 ,1.05],'r',5); % ray 'direction'
v0 = Eval((q0-p0)/Distance(p0,q0)); % Operators: point-point=vector, vector/scalar = vector
Ray(p0,v0,'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, ' same as Eval
end
xlim([-1.5 1.3]); ylim([0 1.7])
clf; disp 'Curve & 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');
% parametric callback with t in [0,1] and dependent variables:
fun = @(t,b0,b1,b2) b0.*(1-t).^2 + 2*b1.*t.*(1-t) + b2.*t.^2;
Curve(b0,b1,b2,fun,'r',2); % A red quadratic Bézier curve
P = Point('P',[.5 .4],'y'); % dist2bezier takes complex values, need to convert:
dist2bezierReal = @(P,A,B,C) dist2bezier(complex(P(1),P(2)),complex(A(1),A(2)),complex(B(1),B(2)),complex(C(1),C(2)));
d = Scalar(P,b0,b1,b2,dist2bezierReal); % dependent scalar value
Circle(P,d,'y'); Text(P,d) % Tangent circle to a curve and radius as text
c1 = Point('c1',[-.25 0],'MarkerSize',5); % adjustable corners
c2 = Point('c2',[1.25 1],'MarkerSize',5); % for the image domain
Image(b0,b1,b2,@dist2bezier,c1,c2,Device='GPU',CallbackType='vectorize');
% Where 'dist2bezier' is a (z,b0,b1,b2) -> real function with complex inputs.
% Image supports CPU and GPU execution with or without input vectorization
% similar to arrayfun. Also accepts real inputs eg.: (x,y,b0,b1,b2) -> real.
% There are limitations and performance considerations, see help for details.
colorbar; xlim([-.25 1.25]); ylim([0 1]) 
Note that you can use any of your existing Matlab funtction and add its output into a custom dependent value inside Geomatplot. Then, you can define Geomatplot objects that depend on it.
clf; disp 'Voronoi and Delaunay triangulation'
n = 30; % number of points
pts = cell(1,n); rng(0);
for i = 1:n
pts{i} = Point(rand(1,2)); % draw draggable points at random
end
pts = PointSequence(pts); % make single pointlist
% Create a dependent delaunay triangulation structure
DT = CustomValue(pts,@delaunayTriangulation);
% Let us draw the triangulation edges
% the edges(dt) function returns a n x 2 index matrix we need to transpose for the right ordering
SegmentSequence(DT,@(dt) dt.Points(edges(dt)',:),'c',3);
% Circumcenters of each triangle in the DT triangulation
PointSequence(DT,@(dt) circumcenter(dt));
% Does not draw boundarys of unbounded regions
SegmentSequence(DT,@drawVoronoi,0,'m',2);
function xy = drawVoronoi(dt)
[C,r] = voronoiDiagram(dt); % kinda stupid but returns inf for all unbounded region vertices
r = cellfun(@(x) [x 1],r,'UniformOutput',false);
xy = C(horzcat(r{:}),:);
end
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.
>> Geomatplot.summary
Geomatplot with 6 movable and 5 dependent plots:
label : type move/stop time value/mean pos | callback
'b0' : mpoint 31.91ms/38.89ms (0.1,0.356) |
'b1' : mpoint 15.30ms/33.11ms (0.642,0.93) |
'b2' : mpoint 19.73ms/27.82ms (0.914,0.276) |
'P' : mpoint 1.27ms/1.30ms (0.518,0.398) |
'c1' : mpoint 0.00ms/0.00ms (-0.25,0) |
'c2' : mpoint 0.00ms/0.00ms (1.25,1) |
'curve1' : dcurve 0.47ms/0.44ms [0.552,0.52] | Curve/internalcallback(b0,b1,b2)
'scal1' : dscalar 0.23ms/0.21ms 0.22167 | Scalar/internalcallback(P,b0,b1,b2)
'circ1' : dcircle 0.28ms/0.31ms c=(0.52,0.4) r=0.22 | f(P,scal1) f=@(t,c,r)c+r*[cos(2*pi*t),sin(2*pi*t)]
'txt1' : dtext 0.47ms/0.37ms " 0.22167" | Text/text_varPos_printDrawing(P,scal1)
'image1' : dimage 19.58ms/34.31ms [0.5,0.5] | Image/img_gpu_cplx_arrayfun(b0,b1,b2)
Methods, Events, Superclasses
The examples/bez.m produces the following:
- Common geometry should be easy to define
- Responsive interaction, fast callbacks
- User callbacks for advanced programmable applets
We showcased the library at CAD'24, see the paper at the proceedings website. If you use Geomatplot for research, please cite this paper. See the BibTeX entry below.
@inproceedings{balint_geomatplot_2024,
author = {Bálint, Csaba and Bán, Róbert},
title = {Geomatplot: Interactive Geometric Plotting Library},
date = {2024-05-09}
url = {http://cad-conference.net/files/CAD24/CAD24-eger.html},
doi = {10.14733/cadconfP.2024.222-226},
shorttitle = {Geomatplot},
eventtitle = {{CAD}'24},
booktitle = {{CAD}'24},
publisher = {U-turn Press {LLC}},
}
Geomatplot is developed by Csaba Bálint and Róbert Bán at Eötvös Loránd University, Budapest, Hungary.