obliqueobject

Obliqueobject is a term used in discussions of oblique geometry and projection to describe a geometric object whose natural description relies on an oblique coordinate frame rather than a standard orthonormal one. The defining feature is that the basis vectors are non-orthogonal, which means coordinates do not directly correspond to orthogonal distances in space.

Mathematically, an oblique object in R^3 can be described with a basis b1, b2, b3 that are not necessarily orthogonal. Any point is expressed as v = x b1 + y b2 + z b3. Distances, angles, and volumes must be interpreted with the ambient metric, not with the coordinate grid, because the basis distorts simple Euclidean relations.

Oblique projection, a central operation for oblique objects, maps a 3D point to a 2D plane by projecting along a direction p that is not perpendicular to the plane. This produces views where depth is skewed but parallelism is often preserved, in contrast to perspective projection which includes convergence.

Common special cases in practice are cavalier and cabinet projections, which are two well-known oblique projections used in technical drawings. In computer graphics and CAD, oblique rendering of an obliqueobject provides a rapid, easily interpreted depiction of shape and orientation.

Applications include technical illustration, education in linear algebra and geometry, and rapid drafting. Underlying theory overlaps with affine transformations and shear mappings, highlighting how changing the oblique basis or projection direction alters perceived shape without changing the underlying object.

Historically, oblique projections emerged in engineering drawing as a practical alternative to perspective, and the obliqueobject label reflects objects described within that framework.