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| Thread ID: 134380 | 2013-06-26 04:47:00 | Drawing a parabola | Tony (4941) | PC World Chat |
| Post ID | Timestamp | Content | User | ||
| 1347036 | 2013-06-26 22:26:00 | I didn't realize a quadratic bezier was a parabola:blush: . It's a long time . . . Not only that, it still is - - and is forecast to continue tomorrow . ;) |
R2x1 (4628) | ||
| 1347037 | 2013-06-26 22:45:00 | 3 point curves in Corel Draw | Whenu (9358) | ||
| 1347038 | 2013-06-27 03:38:00 | 3 point curves in Corel DrawBrilliant! I knew there had to be an easy way. I'll still follow up Terry's suggestions though, just for my own education. | Tony (4941) | ||
| 1347039 | 2013-06-27 03:40:00 | Their parabola is turned through 90 deg compared with the one I envisaged because they are using the equation y=ax² instead of y²=4axWhat I didn't understand was how the formula y=ax² translated into the parameters in the function plotter. | Tony (4941) | ||
| 1347040 | 2013-06-27 04:46:00 | What I didn't understand was how the formula y=ax² translated into the parameters in the function plotter. They are using the equation y = a x², with a=0.5, or as they have re-written it y(t)= 0.5 t² and they are letting t (which has now become T for some reason) go from -4 to + 4 in 100 steps ie in increments of 4-(-4)/100 = 0.08 So for example when x= + 4 and -4, y= 0.5 x 4² =8 The equation for the parabola is stored in Corel draw when the function parameters are specified y(t) and 0.5t² in step 2. Edit: So you calculate the value of a (or 4a) as I previously said and then specify the number of points and the extent over which you want the parabola to draw. (I used 4a, because the 4 comes out of the wash in the standard derivation of a parabola from a conic section, it doesn't matter it is a multiplier constant you determine, so their 'a' is 4 times bigger than the a I used, their a = my 4a) |
Terry Porritt (14) | ||
| 1347041 | 2013-06-27 05:01:00 | This must be screamingly obvious but I just can't see it. If I develop a series of values for a, thus: Y-----X------A 5-----20-----0.3125 4-----16-----0.25 3-----8------0.125 1-----4------0.0625 How does that actually translate to points on the graph? |
Tony (4941) | ||
| 1347042 | 2013-06-27 05:52:00 | So you are using the equation I originally gave y²=4ax So you have now calculated the values of "a" for 4 different parabolas, (actually just to confuse the issue it is 4a you want :) ) You could for example calculate the values of y for x=0 stepping 1 until x=20, ie x=0, 1, 2, 3, .......19,20 You then have pairs of x, y values which you just plot on graph paper, presumably Corel Draw also puts in the x, y axes. It should do it all for you if you specify the function and the range as in the tutorial site you quoted. There is no fundamental difference beyween the tutorial formula and the one I gave, its just transposing the axes to turn the parabola around. |
Terry Porritt (14) | ||
| 1347043 | 2013-06-27 06:13:00 | Just a further note , in the equation y² = 4ax, the physical meaning of 'a' is the distance from the focus of the parabola to the parabola (or parabolic surface) at x=0, y=0. So if you had a parallel beam of light coming onto the paraboloid it would come to a focus at the distance 'a' |
Terry Porritt (14) | ||
| 1347044 | 2013-06-27 08:55:00 | just make sure you keep your pencil on the paper till you've completed the manoeuvre | jayal (1291) | ||
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