| Original Message (ID '81794') By Paul: |
| In Response To 'Re: Parametric regionfunction'
---------
Hello Bill, thanks for replying to my question. I'll try to make my issue somewhat more understandable:
This is the function I'm trying to give a region:
ParametricPlot3D[{{uvlak, vvlak,
100 - 0.00222222 uvlak^2 + 0.00636667 vvlak^2 +
0.000027037 vvlak^3 - 5.46296*10^-7 vvlak^4}}, {uvlak, 0,
150}, {vvlak, -100, 0}]]
The region itself I've got too. This is a parametric function:
x1 = ( (1 - u2 )^2*0 +
2 (u2) (1 - u2)*(150) + (u2 )^2*(150))
y1 = ( (1 - u2)^2*-(100) +
2 (u2) (1 - u2)*-(100) + (u2)^2*0)
(or: b8 = ParametricPlot3D[{{x1, y1, 0}}, {u2, 0, 1}]
When I'm applying this region to my function, it seems like I can't get my region parametric. I think this means I can't get a maximum x(u) at y(u), but a the maximum u at y(u). The same goes for the other orientation.
Below is the code that illustrates this problem. I plotted two Parametric3D plots, each with one part of the region and the region itself (as a line). When the regions are combined in one Plot, it cuts off too much (because of the reason above I think).
b10 = ParametricPlot3D[{{uvlak, vvlak,
100 - 0.00222222 uvlak^2 + 0.00636667 vvlak^2 +
0.000027037 vvlak^3 - 5.46296*10^-7 vvlak^4}}, {uvlak, 0,
150}, {vvlak, -100, 0},
RegionFunction ->
Function[{uvlak, vvlak, zed},
uvlak < (((1 - vvlak + 100)/100)^2*0 +
2 ((1 - vvlak + 100)/100) (1 - (1 - vvlak + 100)/100)*(150) + ((1 - vvlak + 100)/100)^2*(150))
]]
b11 = ParametricPlot3D[{{uvlak, vvlak,
100 - 0.00222222 uvlak^2 + 0.00636667 vvlak^2 +
0.000027037 vvlak^3 - 5.46296*10^-7 vvlak^4}}, {uvlak, 0,
150}, {vvlak, -100, 0},
RegionFunction ->
Function[{uvlak, vvlak, zed},
vvlak > ((1 - (uvlak)/150)^2*-(100) +
2 ((uvlak)/
150) (1 - (uvlak)/150)*-(100) + ((uvlak)/150)^2*0)]]
x1 = ( (1 - u2 )^2*0 +
2 (u2) (1 - u2)*(150) + (u2 )^2*(150))
y1 = ( (1 - u2)^2*-(100) +
2 (u2) (1 - u2)*-(100) + (u2)^2*0)
b8 = ParametricPlot3D[{{x1, y1, 0}}, {u2, 0, 1}]
Show[{b10, b8}, PlotRange -> All]
Show[{b11, b8}, PlotRange -> All]
So I think the mean problem is that I can't get to work my region like a parametric function. Maybe there's a way to get it working like such. |
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