leftimage for poohprod.ru

3D Polygon - draw planes with Matlab


In this example we’re going to explain how to draw a 3D polygon using Matlab. More specifically, we are going to draw several flat surfaces (planes) to build or model a box.

Our main built-in function in this case is the function “fill3”, which is intended to color 3D flat planes.


The sentence fill3(x, y, z, c) would fill the 3D polygon defined by vectors x, y and z with the color specified by c. The vertices of the polygon are specified by coordinates of components of x, y and z, and the polygon is closed by connecting the last vertex to the first one.


Let’s say that we want to draw this arbitrary rectangular box

Drawing a 3D polygon with Matlab

The coordinates of the eight vertices are as follows:

P1(0, 0, 0)
P2(2, 0, 0)
P3(2, 4, 0)
P4(0, 4, 0)
P5(0, 0, 3)
P6(2, 0, 3)
P7(2, 4, 3)
P8(0, 4, 3)

We could draw our first flat surface by filling the area defined by the first four points, like this:


p1 = [0 0 0];
p2 = [2 0 0];
p3 = [2 4 0];
p4 = [0 4 0];

x = [p1(1) p2(1) p3(1) p4(1)];
y = [p1(2) p2(2) p3(2) p4(2)];
z = [p1(3) p2(3) p3(3) p4(3)];

fill3(x, y, z, 1);
xlabel(
'x'); ylabel('y'); zlabel('z');

The code produces this figure:

First plane of the 3D polygon

We can expand our axes, add a grid and hold the image in order to add more planes...

axis([-1 3 -1 5 -1 4])
grid
hold
on

produces...

plane drawn with Matlab. Axex expanded.

We can draw a second surface or plane defined by the last four vertices:


p5 = [0 0 3];
p6 = [2 0 3];
p7 = [2 4 3];
p8 = [0 4 3];


x = [p5(1) p6(1) p7(1) p8(1)];
y = [p5(2) p6(2) p7(2) p8(2)];
z = [p5(3) p6(3) p7(3) p8(3)];
fill3(x, y, z, 2);

And the result now is:

Parallel surfaces for our box in Matlab.

We can add more surfaces by connecting the appropriate vertices, in the correct order. If we continue our code above with

x = [p2(1) p6(1) p7(1) p3(1)];
y = [p2(2) p6(2) p7(2) p3(2)];
z = [p2(3) p6(3) p7(3) p3(3)];
fill3(x, y, z, 3);

x = [p2(1) p6(1) p5(1) p1(1)];
y = [p2(2) p6(2) p5(2) p1(2)];
z = [p2(3) p6(3) p5(3) p1(3)];
fill3(x, y, z, 4);

The resulting 3D-image is the following figure:

4 faces of the box. 3D images


We can produce or generate different views of the same 3D-image, of course:

view(120, 50)

a different view of our 3D polygon


Naturally, we can have a custom-made function to draw rectangles. For example, save something like this:

function poly_rectangle(p1, p2, p3, p4)
% The points must be in the correct sequence.
% The coordinates must consider x, y and z-axes.

x = [p1(1) p2(1) p3(1) p4(1)];
y = [p1(2) p2(2) p3(2) p4(2)];
z = [p1(3) p2(3) p3(3) p4(3)];
fill3(x, y, z, rand(size(p1)));
hold on

We can call that function from any other script or from the command window.

Let’s try it:

poly_rectangle(p3, p4, p8, p7)
poly_rectangle(p1, p4, p8, p5)
view(-155, 43)

What did you get?

From '3D Polygon' to Matlab home

From '3D Polygon' to 3D figures


Top


footer for 3d polygon page

































Related pages


4 band resistor colour codepascals triangle programf table degrees of freedomwhat is a boolean operationsalvage value calculator carmaclaurin series expansion of sinxeuclidean algorithm gcfpiecewise functions in matlabprogram to convert decimal to binaryascii values for alphabetsformula to calculate future valuebest book of electronicsgeometric means formularecursive functions matlabpiecewise function graphsalvage value calculator carmatlab plot circleprime factorization codeprogram to convert binary to octalmethod of bisectiontaylor expansion of tanhmatlab xlswritenonlinear regression matlab examplematrix multiplication in matlabcalculate square feet from inchesmortgage amortmatlab interpndec to binary converterconverting polar to cartesianascii char values3d graphing matlabmatlab function rootsquadratic roots calculatorintegral calculaterhow to draw planes in 3dmatlab gradient functionpythagoras calcpiece wise defined functionsindefinite integral in matlabsolve piecewise functionscircuit nodal analysisbijection methodmatlab 3d surface plot exampleannual depreciation calculatorsolving equations with matlabconversion octal to decimalpythag calculatorbilinear interpolation codehexa to binary converterequation solver matlabformula for maclaurin serieshow to calculate depreciation with residual valuecalculating sq ft from incheshow to find out bmi formulacosine taylor seriesconverting from octal to binarycompounding continuously interest calculatormatlab codes examplescosine expansionsalvage prices for carscalc square feetmatlab zeros functionamortization table calculationgraphs of piecewise functionsint to string matlabinterest compounded continuously formula3n 1 conjecturematlab plot histogramcartesian to spherical converterconvert from cartesian to polarmatlab calculator