Problem2 Surface plots Plot the surface generated by Z sinxc

Problem-2 Surface plots Plot the surface generated by Z sin(x)cos(x)e over the domain x E [-3, 3] and y E [-3,3]. Use meshgrid to generate a grid of X and Y data Plot the surface with (a) meshz (z), (b) waterfall (Z) (c) mesh (X,Y,Z) (d) meshc (x, Y,Z), (e) surf (X,Y,Z) and (f) surf (X,Y,Z) with shading interp Label the plots appropriately Can you describe the observed difference in each of these plots?

Solution

Use meshgrid to generate a grid of X and Y data. Plot the surface mesh and plots.

Sample program to illustrate the different functions:

Example – Displaying Nonuniform Data on a Surface

This example evaluates the sinc function at random points within a specific range and then generates uniformly sampled data for display as a surface plot. The process involves these tasks:

Find below some of the information representing gridded data as surface and mesh plots.

Functions for Plotting Data Grids

MATLAB graphics defines a surface by the z-coordinates of points above a rectangular grid in the x-y plane. The plot is formed by joining adjacent points with straight lines. Surface plots are useful for visualizing matrices that are too large to display in numerical form and for graphing functions of two variables.

Function

Used to Create

mesh, surf

Surface plot

meshc, surfc

Surface plot with contour plot beneath it

meshz

Surface plot with curtain plot (reference plane)

pcolor

Flat surface plot (value is proportional only to color)

surfl

Surface plot illuminated from specified direction

surface

Low-level function (on which high-level functions are based) for creating surface graphics objects

Functions for Gridding and Interpolating Data

These functions are useful when you need to restructure and interpolate data so that you can represent this data as a surface.

Function

Used to Create

meshgrid

Rectangular grid in 2-D and 3-D space

griddata

Interpolate scattered data

griddedInterpolant

Interpolant for gridded data

scatteredInterpolant

Interpolate scattered data

Example: the Use of meshgrid

The use of meshgrid, consider the sin(r)/r or sinc function. To evaluate this function between -8 and 8 in both x and y, you need pass only one vector argument to meshgrid, which is then used in both directions.

The matrix R contains the distance from the center of the matrix, which is the origin. Adding eps prevents the divide by zero (in the next step) that produces Inf values in the data.

Forming the sinc function and plotting Z with mesh results in the 3-D surface.

Emphasizing Surface Shape

MATLAB provides a number of techniques that can enhance the information content of your graphs.

For example: the graph of the sinc function uses the same data as the previous graph, but employs lighting, view adjustments, and a different colormap to emphasize the shape of the graphed function (daspect, axis, view, camlight).

Function	Used to Create
mesh, surf	Surface plot
meshc, surfc	Surface plot with contour plot beneath it
meshz	Surface plot with curtain plot (reference plane)
pcolor	Flat surface plot (value is proportional only to color)
surfl	Surface plot illuminated from specified direction
surface	Low-level function (on which high-level functions are based) for creating surface graphics objects