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Question: How can I find the intersection between a plane f(x,y) and a quadric g(x,z)?

Question:How can I find the intersection between a plane f(x,y) and a quadric g(x,z)?

AndreaAlp 30 Maple 18
surface intersection implicitplot3d ellipse
December 21 2017
2

Hello everyone, 

please need some brain power here to help me with this problem. I'm stacked here and I cannot find a solution. 

I would like to find the intersection between a plane and a quadric surfaces. Please notice that the two equations are written like f(x,y) and g(x,z) respectively. My first problem is that I cannot visualize the two surfaces correctly as implicitplot3d of the quadric surfaces displays nothing in return. 

I want then to find the centre of the ellipse and plot the point and the two surfaces all together in the same 3d plot. Somehow I canont make it. What is wrong with me? 

I am pasting here my MWE. 

Any kind of help would be really appreciated. Thank you so much. 

Andrea

MWE_maple_help.mw
 

> 

restart:
> 

with(plottools):
with(plots):
> 

with(Student:-MultivariateCalculus):
with(Student:-Precalculus):
with(geometry):
> 

with( Optimization ):

> 

my_plane := 2024.30587449691-.341275505799078*x-3.89936179341114*y;
my_quadric := -10595.4104931095+6.73749956241827*x+42.1022818380012*z-0.654818649508000e-1*x^2-0.421174257681115e-1*z^2;

2024.30587449691-.341275505799078*x-3.89936179341114*y

  

-10595.4104931095+6.73749956241827*x+42.1022818380012*z-0.654818649508000e-1*x^2-0.421174257681115e-1*z^2

 (1)
> 

my_quadric_plot_3d := implicitplot3d(my_quadric, x=-10000..10000,
                                       y = -100..100,
                                      z=-10000..10000,color="DodgerBlue"):
my_plane_plot_3d := implicitplot3d(my_plane, x=-10000..10000,
                                       y = -100..100,
                                      z=-10000..10000,color="DarkOrange"):
> 

my_ellipse := CompleteSquare( subs(y = solve(z = my_plane, y), my_quadric));

-0.4211742577e-1*(z-499.8202178)^2-0.6548186495e-1*(x-51.44553815)^2+99.68250

 (2)
> 

ellipse(e1, my_ellipse, [x,z]):
XY_centre_e1     := coordinates(center(o,e1)):
my_center_point := [XY_centre_e1[1],XY_centre_e1[2],
                       subs(x=XY_centre_e1[1], y=XY_centre_e1[2], my_plane)]:
my_center_point_plot := pointplot3d(my_center_point, color = "red"):
> 

display(my_center_point_plot, my_plane_plot_3d, my_quadric_plot_3d);

 


 

Download MWE_maple_help.mw

 

 
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