Compute the position of the car on the road, Computer Graphics

An animation demonstrates a car driving along a road that is given by a Bezier curve along with the subsequent control points: 

Xk

0

5

40

50

Yk

0

40

5

15

The animation finals 10 seconds and the key frames are to be calculated at 1 second intervals. Compute the position of the car on the road at the beginning of the 6th second of the animation.

Solution: By using similar process in the previous exercise we can compute the blending functions as:

1.   B03 = 3!/(0! x (3-0)!) u0(1 - u)(3-0) = 1u0(1 - u)3 = (1 - u)3

2.   B13 = 3!/(1! x (3-1)!) u1(1 - u)(3-1) = 3u1(1 - u)2 = 3u(1 - u)2

3.   B23 = 3!/(2! x (3-2)!) u2(1 - u)(3-2) = 3u2(1 - u)1 = 3u2(1 - u)

4.   B33 = 3!/(3! x (3-3)!) u3(1 - u)(3-3) = 1u3(1 - u)0 = u3

The function x(u) is equivalent to x(u) =   ∑xkBk; here k=0,1,2,3

x(u)       = ∑ xkBk =  x0B03   +   x1B13 + x2B23 +  x2B33

=  (0)(1  -  u)3    +  5  [3u(1  -  u)2]  +  40  [3u2(1  -  u)]  +  50  u3

= 15u(1 - u)2 + 120u2(1 - u) + 50u3

As the same y(u) = y0B03 + y1B13+ y2B23+  y2B33

=  (0)(1  -  u)3    +  40  [3u(1  -  u)2]  +  5  [3u2(1  -  u)]  +  15  u3

= 120u(1 - u)2 + 15u2(1 - u) + 15u3

At the beginning of the sixth second of the animation, that is, when u=0.6, we can utilize these equations to work out such x(0.6) = 29.52 and y(0.6) = 16.92.

The way of the car looks like as:

887_Compute the position of the car on the road.png

Posted Date: 4/4/2013 6:02:30 AM | Location : United States







Related Discussions:- Compute the position of the car on the road, Assignment Help, Ask Question on Compute the position of the car on the road, Get Answer, Expert's Help, Compute the position of the car on the road Discussions

Write discussion on Compute the position of the car on the road
Your posts are moderated
Related Questions
Other curves - parabola and hyperbola Conic sections such as parabola and hyperbola are used in many instances such as in motion planning along a trajectory or in modelling the

1. Using a time Delay Method The delay required between issuing each character to the LCD is about 5-10ms (it's simply known as DELAY). When programming an LCD, a long delay is

Features for good 3-Dimentional modeling software are as: Multiple windows which permit you to view your model in each dimension. Capability to drag and drop primitive

What is bitmap and what is pixmap?  The frame buffer used in the black and white system is called as bitmap which take one bit per pixel. For systems with many bits per pixel,

what languge do computers speak

What are the advantages of rendering polygons by scan line method?  i. The max and min values of the scan were simply found.  ii. The intersection of scan lines with edges i

explain about gks

Transformation for parallel projection Parallel projections is also termed as Orthographic projection, are projections into one of the coordinate planes as x = 0, y = 0 or z

What is homogeneous coordinate? Discuss the composite transformation matrix for two successive translations and scaling. In design and picture formation process, many times

Scientific Visualization This is complex for the human brain to create sense out of the large volume of numbers produced through a scientific computation. Statistical and nume