Oblique Cone

jorge geraldes shared this question 7 years ago
Answered

Hi


How can construct a oblique cone?


Thank´s


Jorge Geraldes

Comments (15)

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1

Hi,


with surface :


Surface[x(C) u + (1 - u) x(A) + r (1 - u) cos(v), y(C) u + (1 - u) y(A) + r (1 - u) sin(v), z(C) u + (1 - u) z(A), u, 0, 1, v, 0, 2 pi]


See list of circles :


x(C) u + (1 - u) x(A) = x(center)

y(C) u + (1 - u) y(A) = y(center)

z(C) u + (1 - u) z(A) = z(center)


r (1 - u) = radius


cos(v) and sin(v) make circle.

https://ggbm.at/1389075

photo
1

hello

i hoped c(2) is a point. is it possible?

c(t)=circle[A,B,C]


saludos4e9c5017d2d8d4e376af982921756a76

photo
1

hello again

a question about the notation: what notation will progress?

create a circle A,B in planeXY

f2b47fe78826b20934f4c4a8d490a9f3


then up and down B

8a0d5826a8b1133a8bc2cf9a06b525b7


the notation change


saludos

photo
1

Hi,


The reason for this is:

* there is no cartesian equation for conics in 3D, so we provide parametric equation

* on our todo list: possibly switch from paramatric to cartesian (when possible) as it's possible for points


Cheers,

Mathieu

photo
1

hello

i hoped c(2) is a point. is it possible?

c(t)=circle[A,B,C]


saludos

what about this?


saludos

photo
1

Does Point[c,2] work?

photo
1

hello

Does Point[c,2] work?


sorry,no

when i saw c(t)=( , , ) I had an illusion during some seconds: c(t):ℝ--------->ℝ³, then I could define d(t,u):ℝ²------->ℝ³


naturally i have tried

Surface[(1 - u) x(D) + u x(Point[c, t]), (1 - u) y(D) + u y(Point[c, t]), (1 - u) z(D) + u z(Point[c, t]), u, 0, 1, t, 0, 6.28319]


and naturally it does not work.


saludos

photo
2

Hello mathmagic,


naturally i have tried

Surface[(1 - u) x(D) + u x(Point[c, t]), (1 - u) y(D) + u y(Point[c, t]), (1 - u) z(D) + u z(Point[c, t]), u, 0, 1, t, 0, 6.28319]


and naturally it does not work.


because surface command doesn't accept commands GGB, just the math functions...


It's possible but not easy...


Surface[x(S) u + (1 - u) x(D) + r (1 - u) (cos(a) cos(v) - sin(a) cos(b) sin(v)), y(S) u + (1 - u) y(D) + r (1 - u) (sin(a) cos(v) + cos(a) cos(b) sin(v)), z(S) u + (1 - u) z(D) + r (1 - u) sin(b) sin(v), u, 0, 1, v, 0, 2pi]


(I have a problem with angles 3D a or b...<180°...normal!)


...

https://ggbm.at/1389097

photo
1

hello

I know how to do curves; my question is : if GG can do (-4.38998, 1.55355, 0) + (-0.77505 cos(t) - 1.78087 sin(t), 5.64937 cos(t) - 0.24432 sin(t), 3.02355 sin(t)) dynamically from A,B,C why I can not use the expression for next calculations?


saludos

PD: more (-4.42415, 1.02285, 1.5537) + (± 0.32628 cosh(t) - 2.35512 sinh(t), ± 0.64844 cosh(t) + 1.37528 sinh(t), ± 0.18058 cosh(t) - 0.68313 sinh(t))

see ±


the bold expression was copied and pasted from GG

photo
1

Hi,


with mathmagic way...


saludos

https://ggbm.at/1389103

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1

hello

great work with texts. I hope GG does this easier like in


https://ggbm.at/1389105


thanks


saludos

photo
1

Hi

You can download an oblique cone in ggb here

http://dmentrard.blogspot.f...

49de38802fe8cb196c66ed9df1571535

Jean

photo
1

Hi

For polyhedra have the tool and command for construct a net, but how can construct


1. a net of cone?


2. a net of cylinder?


Thank´s

photo
1

Hi,


1. a net of cone?


http://tube.geogebra.org/ma...


2. a net of cylinder?


http://tube.geogebra.org/ma...


another examples on GGT...

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1

Thank you very much.

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