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3d sphere coord in 2d

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Ok, I need to project a point on a 3d sphere in a 2d view. Here is the information I have: Bearing & Mark (in degrees) and Radius. Now, I could figure out the location in 3d space (X,Y,Z) and then make a projection matrix to project that onto a 2d surface. I understand all that. What I'm asking here is a simpler way to handle it, since the camera is fixed in this case- straight on the sphere. Is there a simpler way to handle this scenario? Thanks

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Don't know if it is simpler but you could fire a ray from the camera through the point and find the point of intersection with your 2D surface (plane).

This is pretty straightforward and probably cheaper than setting up a matrix and performing a projection.

Just an idea...


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You can project a sphere to screen coordinates using w for calcule radius.
I've got a code from my engine. Let's see:

bool GLeonCamera::ProjectSphere(GLEON_VECTOR3 * origin, GLEON_REAL radius, GLEON_VECTOR3 * projorigin, GLEON_REAL &projradius)
GLEON_VECTOR4 v4temp,v4temp2;
GLEON_VECTOR4 cameraplane;



/////if sphere lie behind of the near plane, don't apply perspective //////transformation
rtemp = GLeonMath::DistancePlanePoint(&cameraplane,origin);

projorigin->x = (1.0f + vtemp.x)*0.5f;
projorigin->y = -(1.0f + vtemp.y)*0.5f;
projorigin->z = vtemp.z;
projradius = radius;
return true;
///////but if sphere is visible, then apply perspective transformation

v4temp.x = origin->x;
v4temp.y = origin->y;
v4temp.z = origin->z;
v4temp.w = 1.0f;

///project point
////total transform is m_matProjection*m_world_to_camera GLeonMath::Matrix4TransformVec4(

return false;////invalid value

projorigin->x = (1.0f + v4temp2.x/v4temp2.w)*0.5f;///scale with W
projorigin->y = (1.0f + v4temp2.y/v4temp2.w)*0.5f;///scale with W
projorigin->z = m_ScissorN+ -rtemp;///ScissorN is the near plane
projradius = radius/v4temp2.w;///scale with W

return true;
///returns a point that x lies in range [0,1]
/// y lies in range [0,1] with y axis pointing down( text direction)
//// and z lies in range [m_frustumN,m_frustumF]

I hope that it help you.

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Illco, ok I can see that. Basically I'm using 2 polar systems in conjunction, one for mark and one for bearing. Hmmmm.

Ok, so now my head explodes on how to combine 2 of them to describe any point on the surface of a sphere...

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