transformable

Transformable is an adjective used in mathematics, geometry, computer science, and engineering to describe objects or systems that can undergo a transformation to produce a different form, position, or state.

In mathematics and geometry, a figure or object is transformable if there exists a mapping that takes it to another figure. Transformations are classified by the properties they preserve. Isometries preserve distances and angles and include translations, rotations, and reflections. Similarities preserve shape up to a uniform scale. Affine transformations preserve straight lines and parallelism while allowing changes in scale and perspective. Transformable objects are often analyzed through the lens of transformation groups acting on a space, revealing invariants and symmetries.

In computer graphics and linear algebra, transformations are typically represented by matrices acting on coordinate vectors. Common operations include translation, rotation, scaling, and shear. A transformable 3D model can be repositioned, deformed, or reoriented by applying a sequence of matrix operations, enabling animation and rendering in different coordinate frames.

In physics and engineering, changing the frame of reference can make certain quantities transformable in predictable ways, preserving the form of physical laws under coordinate changes. In design and robotics, transformable devices or structures can alter their configuration to adapt to tasks or environments, such as reconfigurable furniture or multi-joint robotic systems.

Overall, transformable describes the capacity of an object or system to be altered by a specified class of transformations, with the resulting state governed by the nature of those transformations.