quadric surface การใช้

• Elliptic cones are sometimes considered to be degenerate quadric surfaces as well.
• Quadric surfaces include ellipsoids ( including the sphere ), paraboloids, hyperboloids, planes.
• Which can characterize quadric surfaces located at any center point and aligned along arbitrary axes.
• A quadric surface rotated by an arbitrary angle cannot be represented by any known QGA entity.
• However, QGA includes vector entities that can represent only the principal axes-aligned quadric surfaces characterized by
• A powerful feature of QGA is the ability to compute the intersections of axes-aligned quadric surfaces.
• 5819539783680 The number of twisted cubic curves tangent to 12 given quadric surfaces in general position in 3-space
• It featured constructive solid geometry, support for smooth curved quadric surfaces and a ray-tracer for photo realistic rendering.
• In general, the operation of rotation " does not work " correctly on non-spherical QGA quadric surface entities.
• Representation of general quadric surfaces with useful operations will require an algebra ( that appears to be unknown at this time ) that extends QGA.
• It is a quadric surface, and is one of the possible 3-manifolds which are 4-dimensional equivalents of the conical surface in 3 dimensions.
• Stodola established experimentally that the relationship between these three parameters represented in Cartesian coordinate system has the shape of a degenerate quadric surface, the cone directrix being an ellipse.
• Attempting to rotate a QGA quadric surface may result in a different type of quadric surface, or a quadric surface that is rotated and distorted in an unexpected way.
• Attempting to rotate a QGA quadric surface may result in a different type of quadric surface, or a quadric surface that is rotated and distorted in an unexpected way.
• Attempting to rotate a QGA quadric surface may result in a different type of quadric surface, or a quadric surface that is rotated and distorted in an unexpected way.
• The most famous of these is the polarity or reciprocity of two figures in a conic curve ( in 2 dimensions ) or a quadric surface ( in 3 dimensions ).
• The intersection of two quadric surfaces is in general a nonsingular curve of genus one and degree four, and thus an elliptic curve, if it has a rational point.
• Entities for all principal axes-aligned quadric surfaces can be defined in QGA . These include ellipsoids, cylinders, cones, paraboloids, and hyperboloids in all of their various forms.
• QGA extends CGA to also include representations of some non-spherical entities : principal axes-aligned quadric surfaces and many of their degenerate forms such as planes, lines, and points.
• As in the case of plane analytic geometry, the method of translation of axes may be used to simplify second-degree equations, thereby making evident the nature of certain quadric surfaces.