Curves Representation in Engineering

Flashcards covering key concepts related to curves representation and their mathematical properties in engineering.

Curve

An integral part of design in engineering, applicable to many components in automotive and aerospace industries.

Planar Curve

A two-dimensional curve that lies entirely in a plane.

Curve

An integral part of design in engineering, applicable to many components in automotive and aerospace industries.

Planar Curve

A two-dimensional curve that lies entirely in a plane.

Space Curve

A three-dimensional curve that lies in space.

Smooth Curve

A curve that can be generated by reducing the spacing between data points.

Analytic Curves

Curves represented by mathematical equations such as lines, circles, and conics, allowing easy evaluation and manipulation.

Synthetic Curves

Curves that are useful in designing objects with curved shapes, defined by control points.

Control Points

The set of data points used to define synthetic curves like Bezier curves and splines.

Parametric Curves

Curves represented where each point is expressed as a function of a single parameter.

Cubic Spline

A piecewise cubic function that interpolates a set of data points, guaranteeing smoothness at the data points.

Bézier Curve

A curve defined by a set of control points, using blending functions to determine its shape.

B-Spline Curve

A piecewise polynomial curve that provides local control over segments of the curve.

Quadric Surfaces

Three-dimensional shapes defined by second-degree polynomial equations in three variables.

Ellipsoid

A three-dimensional shape resembling a stretched or squished sphere, defined by a quadratic equation.

Hyperboloid

A surface characterized by equations containing two quadratic terms with opposite signs, resulting in complex geometric structures.