Step-by-Step Process with Code
Step 1: Data Collection
Create a C++ program and input your dataset containing (x, y) points.
C++
#include <iostream>#include <vector>using namespace std;int main(){ // Step 1: Data collection vector<pair<double, double> > dataPoints = { { 1, 2 }, { 2, 3 }, { 3, 1 }, { 4, 5 } }; // Your code here. return 0;} |
Step 2: Parameterization
Assign parameters to data points. Let’s use equidistant parameterization.
C++
// Step 2: Chord-Length Parameterizationstd::vector<double>parameterization(const std::vector<Point>& data){ std::vector<double> param; double total_distance = 0.0; for (size_t i = 0; i < data.size() - 1; ++i) { double dx = data[i + 1].x - data[i].x; double dy = data[i + 1].y - data[i].y; double distance = std::sqrt(dx * dx + dy * dy); total_distance += distance; param.push_back(total_distance); } // Normalize parameters to [0, 1] for (double& p : param) { p /= total_distance; } return param;} |
Step 3: Selecting Control Points
Choose endpoints and possibly a few interior points as control points.
C++
// Step 3: Selecting Control Pointsstd::vector<Point> control_points = { data[0], data[data.size() / 2], data.back() }; |
Step 4: Curve Fitting
Fit cubic polynomials between control points. We’ll use the equations for cubic splines.
C++
// Step 4: Curve Fittingstd::vector<CubicSpline> splines;for (size_t i = 0; i < control_points.size() - 1; ++i) { CubicSpline spline; spline.fit(control_points[i], control_points[i + 1]); splines.push_back(spline);} |
Step 5: Solving for Coefficients
Calculate the coefficients of the cubic polynomials using C++.
C++
// Step 5: Constructing the Cubic Splinedouble t; // Parameter in [0, 1]Point interpolated_point;// Interpolate at a specific parameter value tinterpolated_point = interpolate(splines, t); |
Locating Sampling Points for Cubic Splines
In this article, we will investigate the complexities of locating sampling points for cubic splines. Cubic splines assume a critical part in PC designs, designing, and different logical fields, making it vital to excel at choosing the right focuses for building these smooth and precise bends. Here, we will characterize keywords, furnish bit-by-bit clarifications with code models, and address normal inquiries to extend your comprehension.