Write a MATLAB script M-file named TriangleType that will load a file of triangl

Question

Write a MATLAB script M-file named TriangleType that will load a file of triangles, and use the function from Part 1 to determine if the triangles are acute or obtuse. A message should be printed to the screen for each triangle.

The triangles will be contained in a text file named Triangles.txt. This file will have three columns, one for each side. Every row in the file will correspond to a triangle. The triangles will be either acute or obtuse—there will be no right triangles, nor any non triangles.

Example:
Given a text file with this data:

The script file should produce the following output to the Command Window:

Code Requirements:

The script file must call (use) the function IsAcuteTriangle to determine the type of triangle. No credit will be given if this is done any other way.

The script file must load and use a text file named Triangle.txt with data formatted as specified above.

Helpful hints

Remember to suppress output in both the function & script files.

Create your own Triangles.txt file test your code.

Explanation / Answer

This below m Script code will solve the above problem see the below code

function [VertexNormals,Avertex,Acorner,up,vp]=CalcVertexNormals(FV,N)
%% Summary
%Author: Itzik Ben Shabat
%Last Update: July 2014

%summary: CalcVertexNormals calculates the normals and voronoi areas at each vertex
%INPUT:
%FV - triangle mesh in face vertex structure
%N - face normals
%OUTPUT -
%VertexNormals - [Nv X 3] matrix of normals at each vertex
%Avertex - [NvX1] voronoi area at each vertex
%Acorner - [NfX3] slice of the voronoi area at each face corner

%% Code
disp('Calculating vertex normals... Please wait');
% Get all edge vectors
e0=FV.vertices(FV.faces(:,3),:)-FV.vertices(FV.faces(:,2),:);
e1=FV.vertices(FV.faces(:,1),:)-FV.vertices(FV.faces(:,3),:);
e2=FV.vertices(FV.faces(:,2),:)-FV.vertices(FV.faces(:,1),:);
% Normalize edge vectors
e0_norm=normr(e0);
e1_norm=normr(e1);
e2_norm=normr(e2);

%normalization procedure
%calculate face Area
%edge lengths
de0=sqrt(e0(:,1).^2+e0(:,2).^2+e0(:,3).^2);
de1=sqrt(e1(:,1).^2+e1(:,2).^2+e1(:,3).^2);
de2=sqrt(e2(:,1).^2+e2(:,2).^2+e2(:,3).^2);
l2=[de0.^2 de1.^2 de2.^2];

%using ew to calulate the cot of the angles for the voronoi area
%calculation. ew is the triangle barycenter, I later check if its inside or
%outide the triangle
ew=[l2(:,1).*(l2(:,2)+l2(:,3)-l2(:,1)) l2(:,2).*(l2(:,3)+l2(:,1)-l2(:,2)) l2(:,3).*(l2(:,1)+l2(:,2)-l2(:,3))];

s=(de0+de1+de2)/2;
%Af - face area vector
Af=sqrt(s.*(s-de0).*(s-de1).*(s-de2));%herons formula for triangle area, could have also used 0.5*norm(cross(e0,e1))

%calculate weights
Acorner=zeros(size(FV.faces,1),3);
Avertex=zeros(size(FV.vertices,1),1);

VertexNormals=zeros([size(FV.vertices,1) 3]);
up=zeros([size(FV.vertices,1) 3]);
vp=zeros([size(FV.vertices,1) 3]);
for i=1:size(FV.faces,1)

  
wfv1=Af(i)/(de1(i)^2*de2(i)^2);
wfv2=Af(i)/(de0(i)^2*de2(i)^2);
wfv3=Af(i)/(de1(i)^2*de0(i)^2);
  
VertexNormals(FV.faces(i,1),:)=VertexNormals(FV.faces(i,1),:)+wfv1*N(i,:);
VertexNormals(FV.faces(i,2),:)=VertexNormals(FV.faces(i,2),:)+wfv2*N(i,:);
VertexNormals(FV.faces(i,3),:)=VertexNormals(FV.faces(i,3),:)+wfv3*N(i,:);

if ew(i,1)<=0
Acorner(i,2)=-0.25*l2(i,3)*Af(i)/(e0(i,:)*e2(i,:)');
Acorner(i,3)=-0.25*l2(i,2)*Af(i)/(e0(i,:)*e1(i,:)');
Acorner(i,1)=Af(i)-Acorner(i,2)-Acorner(i,3);
elseif ew(i,2)<=0
Acorner(i,3)=-0.25*l2(i,1)*Af(i)/(e1(i,:)*e0(i,:)');
Acorner(i,1)=-0.25*l2(i,3)*Af(i)/(e1(i,:)*e2(i,:)');
Acorner(i,2)=Af(i)-Acorner(i,1)-Acorner(i,3);
elseif ew(i,3)<=0
Acorner(i,1)=-0.25*l2(i,2)*Af(i)/(e2(i,:)*e1(i,:)');
Acorner(i,2)=-0.25*l2(i,1)*Af(i)/(e2(i,:)*e0(i,:)');
Acorner(i,3)=Af(i)-Acorner(i,1)-Acorner(i,2);
else
ewscale=0.5*Af(i)/(ew(i,1)+ew(i,2)+ew(i,3));
Acorner(i,1)=ewscale*(ew(i,2)+ew(i,3));
Acorner(i,2)=ewscale*(ew(i,1)+ew(i,3));
Acorner(i,3)=ewscale*(ew(i,2)+ew(i,1));
end
Avertex(FV.faces(i,1))=Avertex(FV.faces(i,1))+Acorner(i,1);
Avertex(FV.faces(i,2))=Avertex(FV.faces(i,2))+Acorner(i,2);
Avertex(FV.faces(i,3))=Avertex(FV.faces(i,3))+Acorner(i,3);
  
  
up(FV.faces(i,1),:)=e2_norm(i,:);
up(FV.faces(i,2),:)=e0_norm(i,:);
up(FV.faces(i,3),:)=e1_norm(i,:);
end
VertexNormals=normr(VertexNormals);

for i=1:size(FV.vertices,1)
up(i,:)=cross(up(i,:),VertexNormals(i,:));
up(i,:)=up(i,:)/norm(up(i,:));
vp(i,:)=cross(VertexNormals(i,:),up(i,:));
end

disp('Finished Calculating vertex normals');
end

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