# Mesh plot of data over a parallelogram grid

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Saavanth Velury on 8 Oct 2018
Edited: Nitin Phadkule on 18 Sep 2021
I have a two-dimensional array of numerical values that I am able to create a mesh plot of over a rectangular grid. However, I need a mesh plot of this data over a parallelogram grid instead. The vectors I would like to use to generate this parallelogram are a1 = (1/2,sqrt(3)/2) and a2 = (1/2,-sqrt(3)/2). Is there a way to do this easily? Thank you!

KSSV on 8 Oct 2018
% Coordinates of parallelogram
P0 = [0. 0.] ; P1 = [1. 0.5] ;
P2 = [0 1] ; P3 = [1. 1.5] ;
C = [P0 ;P1 ; P3 ; P2 ; P0] ;
figure
patch(C(:,1),C(:,2),'b')
M = 50 ;
t = linspace(0,1,M) ;
% generate grid
L1 = [P0(1)+(P1(1)-P0(1))*t ; P0(2)+(P1(2)-P0(2))*t] ;
L2 = [P2(1)+(P3(1)-P2(1))*t ; P2(2)+(P3(2)-P2(2))*t] ;
% Mesh
N = 20 ;
X = zeros(M,N) ;
Y = zeros(M,N) ;
t = linspace(0,1,N) ;
for i = 1:M
X(i,:) = L1(1,i)+(L2(1,i)-L1(1,i))*t ;
Y(i,:) = L1(2,i)+(L2(2,i)-L1(2,i))*t ;
end
figure
hold on
plot(X,Y,'r')
plot(X',Y','r')
rui Zeng on 10 Aug 2020
Thank you KSSV, and by using this method we can extend further to connecting irregular shapes by adding more columns for L1 and L2.

Nitin Phadkule on 18 Sep 2021
Edited: Nitin Phadkule on 18 Sep 2021
% just sharing if any one needed for 3d points
% filling parallogram between two position vectors,
% can also an be used to plot and find area of vector addition triangle with
% ommision of x3, y3, z3
% p1=[x1 y1 z1]
% p2=[x2 y2 z2]
% P1+p2=[x1+x2 y1+y2 z1+z2]
p1=[1 -2 3]
p1 = 1×3
1 -2 3
p2=[2 2 0]
p2 = 1×3
2 2 0
x3=p1(1)+p2(1)%x1+x2
x3 = 3
y3=p1(2)+p2(2)%y1+y2
y3 = 0
z3=p1(3)+p2(3)%z1+z2
z3 = 3
patch( [0 p1(1) x3 p2(1) ], [0 p1(2) y3 p2(2) ], [0 p1(3) z3 p2(3) ],[1 0 .1] ,'FaceAlpha',.5,'EdgeColor','none') 