Curves and surfaces Computer Graphics

Question

Create a surface which looks like a vase using parametric spline curves. For this purpose:

1. Use parametric spline equation of your wish to create a curve.

2. Rotate the curve along X or Y axis to create surface. You can also use any

other method to create the surface.

3. Extrude top part of the surface to shorten the surface.

4. Optional: use texture mapping to make the surface look like a real vase.

Answer 1

Video Attached!

close all

clear all

clc

%Get User Input and Make curve

SplineCP = input('How many control points would you like to use: ');

x = [];

y = [];

SplineDisplay = input('would you like to display the points(Y,N): ','s');

for n = 1:SplineCP

Xprompt = horzcat('X', num2str(n), ': ');

x(end+1) = input(Xprompt);

Yprompt = horzcat('Y', num2str(n), ': ');

y(end+1) = input(Yprompt);

if SplineDisplay == 'Y'

close all

scatter(x,y);

end

end

qx = input('How many Query Points would you like to create: ');

xx = linspace(min(x), max(x), qx);

yy = spline(x,y,xx);

if SplineDisplay == 'Y'

close all

plot(x,y,'o',xx,yy)

end

AlignAxis = input('Which Axis do you want your vase along(X,Y,Z): ','s');

ExtrudeDist = input('How long would you like to extrude the top: ');

%Create 3D Geometry

[X,Y,Z] = cylinder(yy);

%Scale Z

Z = Z * max(x);

%Make Bottom

X = vertcat(0*X(1,:), X);

Y = vertcat(0*Y(1,:), Y);

Z = vertcat(0*Z(1,:), Z);

%Extrude Top

X = vertcat(X, X(end,:));

Y = vertcat(Y, Y(end,:));

Z = vertcat(Z, Z(end,:) + ExtrudeDist);

%Rotate Vase

Z2XTransform = [...

0,0,1;

0,1,0;

-1,0,0];

Z2YTransform = [...

1,0,0;

0,0,1;

0,-1,0];

%Z2ZTransform = [...

% 1,0,0;

% 0,1,0;

% 0,0,1];

RandRotMat = (2*rand(3))-1;

%RandRotMat = quat2rotm(randrot());

for n = 1:size(X,1)

for m = 1:size(X,2)

P = [...

X(n,m);

Y(n,m);

Z(n,m)];

if AlignAxis == 'X'

P = Z2XTransform*P;

elseif AlignAxis == 'Y'

P = Z2YTransform*P;

elseif AlignAxis == 'Z'

else

P = RandRotMat * P;

end

X(n,m) = P(1);

Y(n,m) = P(2);

Z(n,m) = P(3);

end

end

%Graphics

Ax1 = axes();

VaseSurface = surf(X,Y,Z);

VaseSurface.EdgeColor = 'none';

axis equal

axis vis3d

Ax1.Color = 'none';

Ax1.AmbientLightColor = '#4DBEEE';

%Texturing

TextureFN = input('What is the Texture File Name: ','s');

TilesX = input('Num X Tiles: ');

TilesY = input('Num Y Tiles: ');

if isempty(TextureFN)

load clown

TextureRaw = ind2rgb(X,map);

else

TextureRaw = imread(TextureFN);

end

TextureScaled = TextureRaw;

if TilesX > 1

for n = 2:TilesX

TextureScaled = horzcat(TextureScaled, TextureRaw);

end

end

TextureRaw = TextureScaled;

if TilesY > 1

for n = 2:TilesY

TextureScaled = vertcat(TextureScaled, TextureRaw);

end

end

VaseSurface.FaceColor = 'texturemap';

VaseSurface.CData = TextureRaw;

VaseSurface.CData = flipud(TextureScaled);