Shape

In geometry, two objects are of the same shape if one can be transformed to another (ignoring color) by dilating (that is, by multiplying all distances by the same factor) and then, if necessary, rotating and translating. Dilation changes the size but not the shape; rotation and translation preserve both size and shape.

Related Topics:
Geometry - Distance - Rotating - Translating - Translation

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In other words, the shape of an object is all the geometrical information that remains after location, scale and rotational effects are filtered out.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Objects which are geometrically similar either have the same shape or one has the same shape as the other's mirror image (or both if they are themselves symmetric).

Related Topics:
Geometrically similar - Mirror image

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

A square

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The shape of an object can be characterized by basic geometry such as points, line, curves, plane, and so on. For an object of greater than 2 dimensions, one can always reduce the dimensions of the shape by considering the shape of a cross-section or a projection.

Related Topics:
Object - Geometry - Point - Line - Curve - Plane - Dimension - Cross-section - Projection

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

An elliptical ring

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The cross-section of a spherical object, for example, will be circular. More complex shapes would, however, generate various curvatures depending on the type of cross-section (e.g. horizontal, vertical). Because of the variation possible in taking cross-section, the orientation of the object is critical.

Related Topics:
Spherical - Circular

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The shape does not depend on changes in orientation/direction. However, a mirror image could be called a different shape. Shape may change if the object is scaled differentially. For example, a sphere becomes an ellipsoid when scaled differently in the vertical and horizontal axis. In other words, preserving axis of symmetry is important for preserving shapes.

Related Topics:
Mirror image - Sphere - Ellipsoid - Symmetry

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Geometric shape is a set of points on the plane R² closed with three or more sides, with one curve or with combinations of them (lines, arcs, circles, elliptical arcs, ellipses, hyperbolas, elliptic curves, ...). -->

Related Topics:
Set - Point - Plane - Side - Curve - Line - Arc - Circle - Elliptical arc - Ellipse - Hyperbola - Elliptic curve

~ ~ ~ ~ ~ ~ ~ ~ ~ ~