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Aug 10, 2024 · A conoid is a ruled surface whose rulings are parallel to a plane (called the directrix plane) and intersect a fixed line (called the axis of the conoid) (Gellert et al. 1989, p. 202).
A conoid is a ruled surface the generatrices of which stay parallel to a plan (P), called directrix plane of the conoid, while intersecting a line (D), called axis of the conoid; it is therefore a Catalan surface.
In geometry a conoid (from Greek κωνος 'cone' and - ειδης 'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions: (1) All rulings are parallel to a plane, the directrix plane. (2) All rulings intersect a fixed line, the axis.
Aug 10, 2024 · A ruled surface is called a right conoid if it can be generated by moving a straight line intersecting a fixed straight line such that the lines are always perpendicular (Kreyszig 1991, p. 87).
Aug 10, 2024 · Plücker's conoid is a ruled surface sometimes also called the cylindroid, conical wedge, or conocuneus of Wallis. von Seggern (1993, p. 288) gives the general functional form as ax^2+by^2-zx^2-zy^2=0, (1) whereas Fischer (1986) and Gray (1997) give z=(2xy)/((x^2+y^2)).
A right conoid as a ruled surface. In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the axis of the right conoid.
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The Right Conoid Surface ∗. See “About Ruled Surfaces” in the Documentation menu. vertical straight line. Perhaps the best known example has . = v cos(u) = v sin(u) = 2 sin(u) e is the “Helicoid”. The formulas in 3DXM deform one into the other �. = x cos(u) = y sin(u) sin(u) + (1 − aa) . with 0 ≤ aa ≤ 1.
