Computer Graphics · Unit 6
Curves and Parametric Representations
Exam-focused notes for Curves and Parametric Representations (Computer Graphics, BIT304): what the TU syllabus asks and how it has actually been tested, with 5 solved past questions from this unit.
What this unit covers
- Parametric curves and properties
- Hermite interpolation and curves
- Bezier curves and properties
- Bezier curve equations and derivations
- Parametric cubic curves
- Curve modeling and animation
Bezier curves and properties
Describe the concept of Bezier curves in 3D modeling. Derive the equation for a Bezier curve and discuss how it is used in curve modeling and animation.[10]
A Bezier curve is a parametric curve defined by a set of control points that influence the shape of the curve without necessarily lying on it. The curve is smooth and continuous, making it ideal for modeling complex shapes in 3D graphics, CAD systems, and a...
Full solved answer →Explain about parametric curve. Describe the properties of Bezier curve. [5]
A parametric curve is a curve defined by parametric equations where the coordinates (x, y) are expressed as functions of a parameter t: - x = f(t) - y = g(t) where t ranges over an interval [a, b]. Instead of expressing y explicitly as a function of x (y = ...
Full solved answer →What is Bezier curve? Describe its properties. [5]
A Bezier curve is a parametric curve used in computer graphics and design to represent smooth curves. It is defined by a set of control points and is generated using the Bernstein polynomial basis functions. The curve passes through the first and last contr...
Full solved answer →Parametric cubic curves
Explain about parametric cubic curve with its properties. [5]
A parametric cubic curve is a curve defined by cubic polynomial equations in parametric form: x(t) = a₀ + a₁t + a₂t² + a₃t³ y(t) = b₀ + b₁t + b₂t² + b₃t³ where t is a parameter (typically t ∈ [0,1]), and a₀, a₁, a₂, a₃, b₀, b₁, b₂, b₃ are coefficients that ...
Full solved answer →Hermite interpolation and curves
Define Hermite interpolation in defining a curve. Draw a line with end points (2, 3) and (12, 8) using DDA.[10]
Definition: Hermite interpolation is a technique for defining a curve using both the endpoints (positions) and the tangent vectors (derivatives) at those endpoints. Unlike simple interpolation that uses only point positions, Hermite interpolation controls t...
Full solved answer →Make Unit 6 stick
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