Cubic vs. Linear Interpolation Methods

This demo was rewritten from the RegularizeData3D examples. This examples shows the difference between the linear and cubic interpolation methods.

clear; close all;

Input points.

inputPoints =[
	1,  0.5, 0.5;
	1,    2,   1;
	1,  3.5, 0.5;
	3, 0.75, 0.5;
	3,  1.5,   1;
	3, 2.25, 0.5;
	3,    3,   1;
	3,    4, 0.5];

Calculate surface with linear and cubic interpolation methods

% Change the spacing to test each axis or both axes. You get the same
% surface profile whether the spacing is 0.5 or 0.01 on either or both
% axes.
x = 0:0.2:4;
y = 0:0.2:4;
 
% Set the smoothness.  See the help for details about the
% smoothness setting.
smoothness = 0.003;
 
% Calculate surface using cubic interpolation
zCubic = regularizeNd(inputPoints(:, 1:2), inputPoints(:, 3), {x, y}, smoothness, 'cubic');
% Other equivalent calls
% zCubic = regularizeNd(inputPoints(:, 1:2), inputPoints(:, 3), {x, y}, smoothness, 'cubic');
% zCubic = regularizeNd(inputPoints(:, 1:2), inputPoints(:, 3), {x, y}, smoothness, 'cubic', 'normal');
 
% Calculate surface using linear interpolation
zLinear = regularizeNd(inputPoints(:, 1:2), inputPoints(:, 3), {x, y}, smoothness);
% Other equivalent calls. If you use [] for smoothness, interp, or solver,
% the default argument is used. See the help
% zLinear = regularizeNd(inputPoints(:, 1:2), inputPoints(:, 3), {x, y}, smoothness, 'linear');
% zLinear = regularizeNd(inputPoints(:, 1:2), inputPoints(:, 3), {x, y}, smoothness, 'linear', 'normal');

Plots

screenSize = get(groot, 'screenSize');

figurePosition = screenSize(3:4)*0.1;

figureSize = [1200 600];

figurePositionAndSize = [figurePosition figureSize];

figure('color', 'w', 'position', figurePositionAndSize)

% Plot this figure on the left.

subplot1 = subplot(1, 2, 1);

view(subplot1,[-74.5, 14]);

grid(subplot1, 'on');

hold(subplot1, 'on');

% Note that surf uses the meshgrid format for plotting surfaces using

% vectors for x and y. regularizeNd outputs in the ndgrid format. In 2d,

% meshgrid is the transpose of the ndgrid format.

surf(x, y, zCubic', 'facealpha', 0.75);

scatter3(inputPoints(:, 1), inputPoints(:, 2), inputPoints(:, 3),[], 'r', 'filled');

xlabel('x', 'FontSize', 12);

ylabel('y', 'FontSize', 12);

zlabel('z', 'FontSize', 12);

title(sprintf('Regularized output surface generated with cubic Interpolation\nOriginal, scattered input points in red'));

axis([0, 4, 0, 4, 0, 1.1]);

% Plot this figure on the right.

subplot2 = subplot(1, 2, 2);

view(subplot2,[-74.5, 14]);

grid(subplot2, 'on');

hold(subplot2, 'on');

% Note that surf uses the meshgrid format for plotting surfaces using

% vectors for x and y. regularizeNd outputs in the ndgrid format. In 2d,

% meshgrid is the transpose of the ndgrid format.

surf(x, y, zLinear', 'facealpha', 0.75);

scatter3(inputPoints(:, 1), inputPoints(:, 2), inputPoints(:, 3), [], 'r', 'filled');

xlabel('x', 'FontSize', 12);

ylabel('y', 'FontSize', 12);

zlabel('z', 'FontSize', 12);

title(sprintf('Regularized Output Surface generated with linear Interpolation.\nOriginal, scattered input points in red'));

axis([0, 4, 0, 4, 0, 1.1]);

% Licensed under the MIT License

% See LICENSE file in project root