Computer Graphics: Finding the position of a lightpen on the face of a CRT

[Crystal037]

Homework Statement

Suppose that a CRT has a square face of 40X40 centimeters and is refreshed in a noninterlaced manner at a rate of 60Hz. Ten percent of the time that the system takes to draw each scan line is used to return the CRT beam from the right edge to the left edge of the screen ( the horizontal-retrace time), and 10 percent of the total drawing time is allocated for the beam to return from the lower-right corner of the screen to the upper-left corner after each refresh is complete (the vertical -retrace time). Assume that the resolution of the display is 1024X1024. Find the relationship between the time at which a lightpen detects the beam and the lightpen's position. Give the results using both centimeters and screen coordinates for the location on the screen

Relevant Equations

time taken for 1 frame to be display = 1/60 sec
time taken for 1 horizontal line to be displayed=(1/60)*(90/100)*(1/1024) ->as 10 percent is used for vertical retrace
time taken for 1 pixel to be displayed= (1/60)*(90/100)*(1/1024)*(90/100)*(1/1024) -> as 10 percent is used for horizontal retrace

This is how I am approaching the problem
let the lightpen be at a position (x,y) and the position to be plotted(x1,y1)
The the time lag =
(1/60)*(90/100)*(1/1024)*(90/100)*(1/1024)*(1024-x)/1024 ->for lightpen to complete the horizontal trace
+ (1/60)*(90/100)*(1/1024)*(1/10) -> for horizontal retrace
+(1/60)*(90/100)*(1/1024)*(90/100)*(1/1024)*(x1)/1024 -> for lightpen to move to the horizontal coordinate of position detected
+ (1/60)*(90/100)*(1/1024)*(1024-y)/(1024) -> for lightpen to complete vertical trace
+ (1/60)*(1/10) -> for vertical retrace
+ (1/60)*(90/100)*(y1/1024) -> for lightpen to move to the vertical coordinate of position detected

In the above equation what if the light pen is in the middle of retracing. I am not able to include that case in my equation.
The relationship in terms of screen coordinates, will it be (y1-y) and (x1-x).
I am not getting how am I supposed to approach this problem

 

[Baluncore]

When is time zero?
Is it when the pixel( 0, 0) is displayed.

 

[Crystal037]

When is time zero?
Is it when the pixel( 0, 0) is displayed.

Yes I think so but does it matter when we are trying to find the relationship between the time at which a lightpen detects the beam and the lightpen's position.

 

[Baluncore]

It may not matter, but it must be defined somewhere. A wise choice may make the process easier.

 

[Tom.G]

Can you see the (few) retrace lines on the screen>

 

[Baluncore]

Can you see the (few) retrace lines on the screen>

I believe this is a hypothetical problem.

 

[pbuk]

I am not getting how am I supposed to approach this problem

Much more simply!

If the light pen is at position (x, y) it detects the beam when the point (x, y) is plotted. This happens when the beam has plotted every row less than y and every pixel in the row y before x.

When is time zero?
Is it when the pixel( 0, 0) is displayed.

We can fix our time base by calling the time when the beam starts in the top left corner $t_0$. The answer will be in the form $t_{x,y} = t_0 + a x + b y + c$.