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Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points.
Form·Z allows design in 3D or in 2D, using numeric or interactive graphic input through either line or smooth shaded drawings ().Modeling features include Boolean solids to generate complex composite objects; the ability to create curved surfaces from splines, including NURBS and Bézier/Coons patches; mechanical and organic forms using the previous as well as metaforms, patches, subdivisions ...
Following is a list of notable software, computer programs, used to develop a mathematical representation of any three dimensional surface of objects, as 3D computer graphics, also called 3D modeling.
An example Bézier triangle with control points marked. A cubic Bézier triangle is a surface with the equation (,,) = (+ +) = + + + + + + + + +where α 3, β 3, γ 3, α 2 β, αβ 2, β 2 γ, βγ 2, αγ 2, α 2 γ and αβγ are the control points of the triangle and s, t, u (with 0 ≤ s, t, u ≤ 1 and s + t + u = 1) are the barycentric coordinates inside the triangle.
A biharmonic Bézier surface is a smooth polynomial surface which conforms to the biharmonic equation and has the same formulations as a Bézier surface. This formulation for Bézier surfaces was developed by Juan Monterde and Hassan Ugail .
Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, [1] potentially generating visually complex objects by combining a few primitive ones. [2] [3] In 3D computer graphics and CAD, CSG is often used in procedural modeling.
SketchUp is a 3D modeling software that is used to create and manipulate 3D models. It is used in architecture and interior design.. SketchUp is owned by Trimble Inc. The software has a free web-based version, and three paid subscriptions to gain access to applications for Windows and macOS.
The generators of any ruled surface coalesce with one family of its asymptotic lines. For developable surfaces they also form one family of its lines of curvature. It can be shown that any developable surface is a cone, a cylinder, or a surface formed by all tangents of a space curve. [5] Developable connection of two ellipses and its development
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