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Solution 110870

Submitted on 11 Jul 2012 by Richard Brown

Correct

48Size
Leading solution size is 36.
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.

Test Suite

Test
Code Input and Output
1
Pass
 
%% Edge case: no vertices
P = zeros(0,2);
P2 = zeros(0,2);
assert(isequal(simplify_polygon(P), P2));

                    
2
Pass
 
%% Edge case: one vertex
P = [1 1];
P2 = [1 1];
assert(isequal(simplify_polygon(P), P2));

                    
3
Pass
 
%% Edge case: three vertices (a single line segment)
P = [...
    1 1
    1 2
    1 1 ];
P2 = [...
    1 1
    1 2
    1 1];
assert(isequal(simplify_polygon(P), P2));

                    
4
Pass
 
%% Single line segment with multiple vertices
P = [ ...
    1 1
    2 1
    3 1
    4 1
    5 1
    4 1
    3 1
    2 1
    1 1];
P2 = [ ...
    1 1
    5 1
    1 1];
assert(isequal(simplify_polygon(P), P2));

                    
5
Pass
 
%% Single line segment, different spacing
P = [ ...
    1 1
    2 1
    4 1
    5 1
    1 1];
P2 = [ ...
    1 1
    5 1
    1 1];
assert(isequal(simplify_polygon(P), P2));

                    
6
Pass
 
%% Rectangle
P = [ ...
    1 1
    2 1
    3 1
    4 1
    4 2
    4 3
    3 3
    2 3
    1 3
    1 2
    1 1];
P2 = [ ...
    1 1
    4 1
    4 3
    1 3
    1 1];
assert(isequal(simplify_polygon(P), P2));

                    
7
Pass
 
%% Two rectangles separated by line segment
P = [ ...
    1 2
    1 1
    2 1
    2 2
    1 2
    1 3
    1 4
    1 5
    2 5
    2 4
    1 4
    1 3
    1 2];
P2 = [ ...
    1 1
    2 1
    2 2
    1 2
    1 5
    2 5
    2 4
    1 4
    1 1];
assert(isequal(simplify_polygon(P), P2));

                    
8
Pass
 
%% Nonsimple polygon (figure eight)
P = [ ...
    1 1
    2 2
    3 3
    1 3
    2 2
    3 1
    1 1];
P2 = [ ...
    1 1
    3 3
    1 3
    3 1
    1 1];
assert(isequal(simplify_polygon(P), P2));

                    
9
Pass
 
%%
P = [ ...
    1 1
    2 2
    3 3
    4 4
    5 5
    5 4
    6 3
    8 1
    7 1
    1 1];
P2 = [ ...
    1 1
    5 5
    5 4
    8 1
    1 1];
assert(isequal(simplify_polygon(P), P2));

                    
10
Pass
 
%% Circle; no points should be removed
theta = linspace(0,2*pi,200);
theta(end) = 0;
x = 20*cos(theta);
y = 20*sin(theta);
P = [x', y'];
P2 = P;
assert(isequal(simplify_polygon(P), P2));

                    
11
Pass
 
%% Starting vertex can be removed
P = [ ...
    2 1
    3 1
    3 2
    3 3
    2 3
    1 3
    1 2
    1 1
    2 1];
P2 = [ ...
    3 1
    3 3
    1 3
    1 1
    3 1];
assert(isequal(simplify_polygon(P), P2));