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graphicsgeometryraytracing

Cone normal vector

I have cone->p (vertex of the cone), cone->orient (axis vector), cone->k (half-angle tangent), cone->minm and cone->maxm (2 height values, for cone caps). Also I have point intersection which is on the cone. How do I find the cone (side surface) normal vector at intersection point using only these parameters?

Solution

  • Сame up with simpler method:

    Find distance Dis from intersection point I to base P

    Make axis orientation vector of length

    D = Dis * sqrt(1+k^2)

    and make point on axis at this distance

    A = P + Normalized(Orient) * D

    Now

    Normal = I - A

    enter image description here

    Old answer:
    Make orthogonal projection of point I (intersection) onto cone axis using vector `IP = I - P' and scalar (dot) product:

    AxProj = P + Orient * dot(IP, Orient) / dot(Orient, Orient)

    Vector from AxPr to I (perpendicular to axis):

    AxPerp = I - AxProj

    Vector, tangent to cone surface, using vector product:

    T = IP x AxPerp

    Vector, normal to cone surface:

    N = T x IP

    enter image description here