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Computer graphics

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Computer graphics

  1. The worldThe world coordinate system is a unique system that is liner along all axes, which can include the feet units, mill bars, and different calculations. This system occurs in three-dimension like the world is covered in three-dimension not two-dimension which are expressed by real numerical.
  2. Region filling

Seed filling

Boundary filling

  1. This is the algorithmic way of developing a texture mathematically whereby it can create précised textures in either three-dimension or two-dimension. This approach can lower the storage cost and also use unlimited texture resolution.
  2. Rational B-spline modeling which is based on geometric forms and technology.

Polygonal modeling which involves the x, y and z coordinates to form different surface and shapes which can be combined to give a model shape.

Primitive modeling: this is the modeling of shapes like cubes to bring up a variation of two shapes into the desired shape.

  1. A world view coordinates with coordinate x,y and z can be represented in view coordinates by translating the reference viewpoint e to the origin, rotation about the world coordinate y-axis to bring the view to the yz plane, align the z-axis by rotating the x-axis coordinate and then rotating about the world coordinates z-axis to align the y-axis with reflection.

 

  1. This is the physical way of measuring coordinates in pixels using the current screen computer resolution. According to the screen coordinates, the point of origin (0,0 ) is located in the upper left side of the viewing area in which they coordinates above the x-axis increases in positive numbers, and the x coordinates increase with negative numbers to the y axis on the right.
  2. True

8a) implicit curve: This is a curve that is defined by implicit equation that relates two variables x and y whereby both of them are dependent and independent to each other.

  1. b) Explicit curve: This is a function that is represented with independent variables which I s expressed in the form y=(fx). The y variables is independent to the x variables.
  2. c) Parametric curve: This is the use of the variable t that is involved in the equation y=f(x) in separate equation in terms of t. the third variable t is known as the parameter while the whole equation in terms of t is known as the parametric equation.
  3. d) Spline curve: This is a piecewise line which is expressed mathematically to allow the collection of control points in which the user is allowed to enter sequence points and curve contraction to produce a complex curve and surfaces.

9 R=radius

PC=point of curvature

PT=point of tangency

POC=point of curve

POT=point of tangent

LC=long chord

T=tangent distance

D=degree of curve

  1. This is a digital imaging technique that reduces the visual defects whenever a defection of high-resolution image is represented in a low resolution. Antialiasing makes smooth lines by adding discoloration on the line edges or the object to cause the jagged edges blur and melt so as when the human eye is zoomed it will no longer notice the discoloration created there. When the output devices does not have a high resolution which represent a smooth line the jaggies upper which is a problem in the computer monitor.

Diagram

 

  1. True

12.p1=(2,5)

P2=(2,10)

X1=2, y1=5, x2=2, y2=10

Dx=2-2=0

Dy=10-5=5

M=dy/dx=5/0=5

P1=(2,5), p2=(3, 10) p3(4,15), p4(2,10)

13 .p1=(5,4)

P2=(12,17)

X1=5, y1=4, x2=12, y2=17

Dx=12-5=7

Dy=17-4=13

M=dy/dx=13/7=13/7

P1=(5,4), p2=(6, 8) p3(7,12), p4(2,10)

14.x1=2, y1=5, x2=2, y2= 10

Dx=2-2=0

Dy=10-5=5

L1=2*dy=2*0=0

L2=2*dy-dx=2*5=10

D=L1-dx=0-0=0

P1=(2,5), p2=(3,5), p3( 4,6) p4(5,6)

 

  1. This is the calculation of a circle perimeter of the first octant to produce the other octant since the other points are taken as a mirror points due to the circle being symmetrical. This algorithm has a circle equation which is in the equation x2+y2=r2 in which it has the center (0, 0).

15b)enter center h=0 and k=0 and r=5

D=1-5=-4

Take x=0, y= 5

If d>=0 then x=x+1 and y =y-1; d=d+2*(x-y)+5

Id d<0 then x=x+1 and d=d+2*x+3;

Where to stop: x or y=5/sqrt2 =5/1.414=4

Mp circle algorithim (0,5)=1-5=-4: pixel=(0,5)

(1,5)=-4+2*1+3=1: pixel=(1,5)

(2,4)=1+2*2(2-4)=2=pixel =(2,4)

Stop;

 

  1. CD= partialy inside=x=x1+x1u,

y=y2-x1(u)

GH= completely inside=y=y1+slope*(x-x1)

=x=x1+(1/slope)*(y-y1)

EF= partially inside: calculation = x=x1+u(x2-x1),

x=x1+u(dx),

y=y1+u(y2-y1),

y=y1+u(dy)

 

  1. This is the removal of portion parts of strings which are outside the plane view. This method can be applied depending on the character by selecting different clipping text. The diagram below shows the text clipping whereby if the character is inside the widow then we consider it but if not the character is removed.

Diagram

String

                               School   

Stock                                                                    

Befor clipping

ing

                                   School

ock     

After clipping

 

 

 

References

Rogers, D. F. (1990). Mathematical elements for computer graphics.

Liang, Y. D., & Barsky, B. A. (1984). A new concept and method for line clipping. ACM Transactions on Graphics (TOG)3(1), 1-22.

Hummel, W., Hauser, J., & Bürgi, H. B. (1990). PEANUT: Computer graphics program to represent atomic displacement parameters. Journal of Molecular Graphics8(4), 214-220.

 

 

 

 

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