I have a sequence of geometric items that I need to join smoothly to create a smooth path. When points are far enough apart, they will be joined by a straight line. When they are too close together, the number of close points are joined by an interpolating cubic B-spline. How can I design the Bspline so that the joining point between a straight line and Bspline is C2 continous? I will be using the algorithm A9.2 SolveTridiagonal from The NURBS Book to generate the cubic interpolating spline. This algorithm depends on setting the first derivatives at the endpoints. I could easily set the first derivatives at the endpoints to have equal directions as the straight lines, but is this enough to guarantee what I want? Or do I need a specific magnitude for these derivatives?
2026-03-27 01:46:15.1774575975
How can I make sure that a line and spline join smoothly (C2 continuity)?
200 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GEOMETRY
- Point in, on or out of a circle
- Find all the triangles $ABC$ for which the perpendicular line to AB halves a line segment
- How to see line bundle on $\mathbb P^1$ intuitively?
- An underdetermined system derived for rotated coordinate system
- Asymptotes of hyperbola
- Finding the range of product of two distances.
- Constrain coordinates of a point into a circle
- Position of point with respect to hyperbola
- Length of Shadow from a lamp?
- Show that the asymptotes of an hyperbola are its tangents at infinity points
Related Questions in CONTINUITY
- Continuity, preimage of an open set of $\mathbb R^2$
- Define in which points function is continuous
- Continuity of composite functions.
- How are these definitions of continuous relations equivalent?
- Show that f(x) = 2a + 3b is continuous where a and b are constants
- continuous surjective function from $n$-sphere to unit interval
- Two Applications of Schwarz Inequality
- Show that $f$ with $f(\overline{x})=0$ is continuous for every $\overline{x}\in[0,1]$.
- Prove $f(x,y)$ is continuous or not continuous.
- proving continuity claims
Related Questions in SPLINE
- Approximate spline equation with Wolfram Mathematica
- Almost locality of cubic spline interpolation
- inhomogeneous coordinates to homogeneous coordinates
- Can the relocation of one control point of a NURBS curve be compensated by an adjustment of some weights?
- How to construct a B-spline from nodal point in Matlab?
- Evaluation the interpolation polynomial at $x$
- Book suggestions on B-spline method for solving differential equations
- C2 continuous Bezier contour.
- Formula for the partial derivative of a bivariate tensor-product spline on a grid of points
- Integral of two zero-order spline basis functions
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?