Conical Surface Class

System Object
Autodesk.Revit.DB Surface
Autodesk.Revit.DB ConicalSurface

	Name	Description
	Axis	Axis of the cone. This is the Z axis of the local coordinate system associated with this cone.
	HalfAngle	Cone angle.
	IsValidObject	Specifies whether the .NET object represents a valid Revit entity. (Inherited from Surface )
	OrientationMatchesParametricOrientation	Indicates whether this Surface's orientation is the same as or opposite to its parametric orientation. (Inherited from Surface )
	Origin	Apex of the cone. This is the origin of the local coordinate system associated with this cone.
	XDir	X axis of the local coordinate system associated with this cone.
	YDir	X axis of the local coordinate system associated with this cone.

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	Name	Description
	Create	Creates a conical surface defined by a local reference frame and a half angle.
	Dispose	(Inherited from Surface )
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object )
	GetBoundingBoxUV	Gets the UV bounding box of the surface. (Inherited from Surface )
	GetFrameOfReference	Returns frame of reference associated with this ConicalSurface.
	GetHashCode	Serves as the default hash function. (Inherited from Object )
	GetType	Gets the Type of the current instance. (Inherited from Object )
	IsCoincidentWith	Determine if two surfaces are coincident (ignoring Envelopes). For an affirmative answer, the surfaces must have the same type (e.g., two planes). (Inherited from Surface )
	IsValidConeAngle	Checks whether the input value lies is not 0, greater than -PI/2 and lesser than PI/2.
	Project	Project a 3D point orthogonally onto a surface (to find the nearest point). Throws InvalidOperationException if the projection fails. (Inherited from Surface )
	ProjectWithGuessPoint	Project a 3D point orthogonally onto a surface (to find the nearest point). This method is meant to be used when a good approximate solution for the projection is available. Throws InvalidOperationException if the projection fails. (Inherited from Surface )
	ToString	Returns a string that represents the current object. (Inherited from Object )

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The parametric equation of the cone is S(u, v) = center + v*[sin(halfAngle)(cos(u)*xVec + sin(u)*yVec) + cos(halfAngle)*zVec]. Only the branch of the cone with v >= 0 should be used.

Reference