com 366

COM 366

Reading Data

COM 366

Reading data from disc files

Organise the data in a logical fashion with comments as necessary.

#Data for a cube# First the link data121,22,33,44,11,52,63,74,85,66,77,88,5#Now the node data81,-1,1-1,-1,1-1,1,11,1,11,-1,-1-1,-1,-1-1,1,-11,1,-1

#Data for a cube# First the link data121,22,33,44,11,52,63,74,85,66,77,88,5#Now the node data81,-1,1-1,-1,1-1,1,11,1,11,-1,-1-1,-1,-1-1,1,-11,1,-1

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Open filename For Input As #1 Input #1, temp_line While Left$(temp_line, 1)= "#"

Input #1, temp_lineWend

num_lines = Clnt(temp_line) ReDim L(2, num_lines)

For i = 1 To num lines Input #1, L(1, i), L(2, i)

Next i input #1, temp_line While Left$(temp_line, 1)= "#"

Input #1, temp_line Wend

num_points = Clnt(temp_line) ReDim X(num_points), Y(num_points), Z(num_points) For i = 1 To num_points

Input #1, V(i).X, V(i).Y, V(i).Z Next i

Close #1

A simple procedure to read the text file

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Topic 6

Data structures revisited

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(a) (b) (c) (d)

Figure 6.1

Representing Objects with polygons

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OBJECTOBJECT

Node # Co-ordinates

V1

V2

V3

Vm

x1,y1,z1

x2,y2,z2

x3,y3,z3

xm,ym,zm

Figure 6.2 : Object Data Structure

FACE LIST

V1,V2,V3,....

V2,V3,V12,....

V6,V3,V9,....

V11,V21,V3,....

Face #

F1

F2

F3

F4

Properties

Colour, textureAppearance etc.

“

“

“

Data structure for an object

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X

Y

Z

CO

X

X

Y

Y

Z

Z

H1O

H2O

GO

X

Y

Z

Figure 6.3

Local & global co-ordinates

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Scene

Object 1 Object 2 Object 3

Lighting Cameraview

Figure 6.4

Data structure for a scene

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Figure 6.5

Sweep generation of an object

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N = 6

N = 30

Axis of symmetry

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function RevObject(n)

%To generate a 3D object from profile in 'goblet.txt'

%NOTE this version only works with 5 nodes in the profile

%First read in the data, set the number of nodes and faces

U = dlmread('goblet.txt');

[a,b] = size(U);

numnodes = a*n;

numpatch = (a-1)*n;

Node = zeros(numnodes,3);

PSet = zeros(numpatch,4);

%Now calculate all the node values

for k = 0:n-1

for L = 1:a

theta = 2*k*pi/n;

Node(L+a*k,1) = U(L,1)*cos(theta);

Node(L+a*k,2) = U(L,1)*sin(theta);

Node(L+a*k,3) = U(L,2);

end;

end;

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for k = 1:n

term = 5*(k-1);

for L = 1:4

Pset(4*(k-1)+L,:) = [(term+L) (term+L+1) (term+L+6) (term+L+5)];

end

end;

%Finally ensure that the last but one profile connects to the first

for k = numpatch-3:numpatch

Pset(k,3)=Pset(k,3)-numnodes;

Pset(k,4) = Pset(k,4) - numnodes;

end

%Uncomment the following line if you want to see the patch array

%Pset

patch('Vertices',Node,'Faces',Pset,'facevertexCdata',[0.2 0.2 1],'facecolor','flat')

axis square

rotate3d on

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A B X

Figure 6.3

Constructive solid geometry - 1

X A B

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X A B

A B X

Figure 6.4

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X A B


A B A - B

Figure 6.5

B - A

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[X,Y,Z] = cylinder

[X,Y,Z] = cylinder(r)

[X,Y,Z] = cylinder(r,n)

Three forms of the cylinder function

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function [X,Y,Z] = Cone(R,h,L)%To create X,Y,Z data to draw a truncated cone.%R = base radius of the cone.%h = height to which the cone is drawn%L = apex of the cone%Note setting h = L will draw the full coneif nargin < 3, L = 1; endif nargin < 2, h = L; endif nargin == 0, R = 1; endstepsize = h/10;t = 0:stepsize:h;[X,Y,Z] = cylinder((R*(1-t/L)));

L

tRr 1.

When t = 0 then r = R

When t = L then r = 0

Generating a cone

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h = L h < L

Examples of cone

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Superquadratics

Example the super ellipse

)(sin.

)(cos.

m

m

by

ax

m = 1 gives a normal ellipse

m >1 gives a cusped figure

m < 1 gives a ‘fatter figure

m = 0 gives a rectangle

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Superquadratics in 3D (superquad)

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Using Fractals

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The Koch Curve

N=0N=1

N=2 N=5

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Length of the Koch Curve

N = 1 2 3 …………… m

33.13

1.4 78.1

9

1.16 37.2

27

1.64

length then As m

mm

3

1.4

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Dimension of the Koch Curve

Definition of space dimensionIf N is the number of self similar copies required when an object is scaled by r then the

Dimension of the object ‘D’ is given by :

1 = NrD

If a line is scaled by 1/3 then 3 copies are required thus the

dimension of a line is 1 = 3(1/3)D. Therefore D = 1

If a square is scaled by 1/3 then 9 copies are required thus the

dimension of a square is 1 = 9(1/3)D. Therefore D = 2

For the Koch curve if we scale by 1/3 we require 4 sections and the dimension is

2857.1)3log(

)4log(D

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Using ‘graftals’The correct name is parallel graph grammars

Definitions (you can improvise your own)

1. A AA

2. B A[B]AA[B]

3. [ ] means ‘branch left

If we start with A we generate a dull sequence A AA AAAA etc. But lets start with B and

Record the first 3 generations :

(0) B (1) A[B]AA[B] (2) AA[A[B]AA[B]]AAAA[A[B]AA[B]]

B

B

B

A

A

A

B B

B B

A

A

A

A

A

A

AAA

AAA

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Change the angle between turns and introduce () to mean branch right and we start to

Get more interesting shapes

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Use curved segments and colour Finally add some random

variation in angles and lengths

Making ‘graftals’ realistic

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Modelling mountains

RxxPyyy

xxx

iiiinew

iinew

.2

12

1

11

1

P is a perturbation based on the length ‘s’ of the line e.g. 2-s and R is a random number between 0 and 1

0 1 2

In three dimensions the concept is exactly the same but using a triangle or pyramid as a starting point

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Add some colour and and shading !

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Topic 7

Hidden Surface Removal

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Convex Solids

A solid is convex if a straight line joining any two points on the surface passes entirely through the body of the solid or through its surface.

Examples of common convex solids include :

Sphere, cube, cone, cylinder, pyramid

All remaining solids are non convex

N

L Towards the viewer

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Criteria of Visibility

The polygon surface is visible if

0 90o or 270o 360o

Or in terms of the angle cosine Cos() 0

NL

NL

.cos

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L = (Lx,Ly,Lz)

Numerical evaluation of the visibility condition

Viewing direction

N = (Nx,Ny,Nz) Surface normal

If these two vectors are of unit length then

|L| = |N| = 1

L N L L L N N N L N L N L Nx y z x y z x x y y z z ( , , ) ( , , )

When viewing along the z axis L reduces to (0,0,-1)

cos( ) N z 0 0 or N z

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Programming the visibility criterion

My recommendation is that you add all the normals to your data structure (NX,NY,NZ) and then rotate them with the nodes before applying the visibility criterion

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Hidden Surface Removal for Non Convex Objects

The painters ( or z buffer) algorithm

If we can, in an unambiguous manner, sort the polygons into order of increasing z values then we can correctly render the object by drawing the polygons with the largest z values first. Remember that for a left handed co-ordinate system the polygons with the largest z value will be the furthest from the view point.

Test 1 : Do the X extents of P and Q not overlap ?

Test2 : Do the Y extents of P and Q not overlap ?

Test3 : Is P completely on the side of the plane of Q away from the viewer ?

Test4 : Is Q completely on the side of the plane of P nearer to the viewer ?

Test5 : Do the projections of the two polygons on the viewing plane not overlap ?

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The depth buffer method

This method like the z buffer algorithm begins with a list of polygons but makes no attempt to sort the polygons by z depth instead two pixel based buffers are created. For each pixel position we store the current pixel colour in one buffer. The second buffer contains a single z value at each pixel position representing the depth of the currently displayed pixel.

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For all pixels Set pixel_colour = background Set pixel_depth = maximum_valueEnd for all pixels

For each polygon For each projected_polygon_pixel If z_co_ord < pixel_depth then Set pixel_colour = ploygon_colour Set pixel_depth = z_co_ord Endif End for each projected_polygon_pixel

End for each polygon

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Type Vector x as

single y as

single z as

singleEnd type

Type Vector x as

single y as

single z as

singleEnd type

Type PolygonN as vectorCR as integerCG as integerCB as integerV() as integer

End Type

Type PolygonN as vectorCR as integerCG as integerCB as integerV() as integer

End Type

GLOBAL Object() as integer ‘The array of polygon numbers

GLOBAL Poly() as Polygon ‘ The array of polygons

GLOBAL Node() as Vector ‘ The array of vertex co-ordinates

GLOBAL num_polygons, num_nodes as integer.

GLOBAL Object() as integer ‘The array of polygon numbers

GLOBAL Poly() as Polygon ‘ The array of polygons

GLOBAL Node() as Vector ‘ The array of vertex co-ordinates

GLOBAL num_polygons, num_nodes as integer.

Programming in VB

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