3d cone equation

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Hi,

For the new version if my particle system I want to have cones as possible spawn volumes as well as for determining the spawn velocity. What is the equation of such a cone?

1. Given the top is in 0,0,0 and the height from top to the (circle shaped) bottom is aligned to the x-axis.

-What is the equation for a point X,Y,Z exactly on the bottom circle of the cone?
- And the equation for a point inside the cone?

2. Given the top in a random point Xr,Yr,Zr and the height vector oriented in a random direction (vector is onow):

- equation for point on the bottom of the cone?
- equation for point inside the cone?

I wasn't able to figure it out on myself.. Hopefully someone can help me out.. I should be able to figure out how to randomly choose a point on or in the cone, mainly for the particles velocity..

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Hi,

For the new version if my particle system I want to have cones as possible spawn volumes as well as for determining the spawn velocity. What is the equation of such a cone?

1. Given the top is in 0,0,0 and the height from top to the (circle shaped) bottom is aligned to the x-axis.

-What is the equation for a point X,Y,Z exactly on the bottom circle of the cone?
- And the equation for a point inside the cone?

2. Given the top in a random point Xr,Yr,Zr and the height vector oriented in a random direction (vector is onow):

- equation for point on the bottom of the cone?
- equation for point inside the cone?

I wasn't able to figure it out on myself.. Hopefully someone can help me out.. I should be able to figure out how to randomly choose a point on or in the cone, mainly for the particles velocity..

Without a height for the cone you can't get a point on the bottom face.

You can take the direction from apex to center of base, an angle around the circumference of base[0:360], an angle denoting cone radius[0:n], to get a vector that is inside cone.

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Sry, it was late, so I forgot to mention: Not only is the top point and the direction of the height given, but also the length of the height and the angle of the cone (determining the radius of the bottom circle). Given all that things, what is the equation I'm looking for? Thanks!

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