As I know it, a periodic function is a function that repeats its values in regular intervals or period. However Bézier curves can also be periodic which means closed as opposed to non-periodic which means open. How is this related or possible?
2026-03-28 02:23:32.1774664612
How can a Bézier curve be periodic?
493 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPUTATIONAL-GEOMETRY
- Least Absolute Deviation (LAD) Line Fitting / Regression
- Why is the determinant test attractive for the Convex Hull algorithm?
- Geometry of the plane in 3D and cross product
- How can I give a polygon with exactly a given number of triangulations?
- How to draw an equilateral triangle inscribed in another triangle?
- An enclosing polygon with minimum area
- Merging overlapping axis-aligned rectangles
- Find algorithm to produce integer points in a polygon
- Closest line to a set of lines in 3D
- Why do we check $n^2 - n$ pairs of points in SlowConvexHull algorithm?
Related Questions in BEZIER-CURVE
- Sweet spots for cubic Bezier curve.
- C2 continuous Bezier contour.
- Design an algorithm to check if point lies on a Bézier curve
- What is the equation of a reflected Bézier curve?
- Solving the bezier curve equation is giving wrong value
- Bézier control points for drawing an interpolating cubic spline *function*
- Tangent of Cubic Bezier curve at end point
- How to tell if a 2d point is within a set of Bézier curves?
- Converting polynomial interpolations to Bézier splines
- Bezier Curve and derivatives
Related Questions in PERIODIC-FUNCTIONS
- Is the professor wrong? Simple ODE question
- The system $x' = h(y), \space y' = ay + g(x)$ has no periodic solutions
- Show that a periodic function $f(t)$ with period $T$ can be written as $ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $
- Is $x(t) = \sin(3t) + \cos\left({2\over3}t\right) + \cos(\pi t)$ periodic?
- To show $\int_{a}^{a+T} f(x)dx$ is independant in $a$
- Is the function $f(t)=\sin(\omega_0 t+\phi_0(t))$ periodic?
- Periodic function notation, need help with a fundamental concept
- Time dependent differential equation system with periodicity
- Let $f: \mathbb{R} \to \mathbb{R}$ and $\exists \ \ b \in \mathbb{R} : f(x+b)=\sqrt{f(x)-f^2(x)}+\frac{1}{2}$
- Compute the period of this function $f(x)=7+3\cos{(\pi x)}-8\sin{(\pi x)}+4\cos{(2\pi x)}-6\sin{(2\pi x)}$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
A curve $C$ parameterised over the interval $[a,b]$ is closed if $C(a) = C(b)$. Or, in simpler terms, a curve is closed if its start point coincides with its end-point. A Bézier curve will be closed if its initial and final control points are the same.
A curve $C$ is periodic if $C(t+p) = C(t)$ for all $t$ ($p \ne 0$ is the period). Bézier curves are described by polynomials, so a Bézier curve can not be periodic. Just making its start and end tangents match (as J. M. suggested) does not make it periodic.
A spline (constructed as a string of Bézier curves) can be periodic.
People in the CAD field are sloppy in this area -- they often say "periodic" when they mean "closed".