Hilbert curve program in CIn this article, we will discuss the Hilbert curve program in C. But before discussing the program, we must know about the Hilbert curve. Hilbert Curve:The Hilbert Curve is a fractal spacefilling curve that passes through each point in a square in a predetermined order. David Hilbert, a mathematician, was introduced it for the first time in 1891. Recursively breaking the square into smaller squares and then connecting these smaller squares in a way that creates a continuous curve is the main notion behind the Hilbert Curve. Order of the Curve:The order of the Hilbert Curve controls how many recursive steps must be taken to produce the curve. The curve gets increasingly complex and convoluted as the sequence increases. The curve's order is often represented by the positive integer "n". Construction of the Curve:The Hilbert Curve is built via recursive subdivision and rotation. Four smaller curves, one for each of the square's four quadrants, make up each level of recursion. The order in which these quadrants are visited is carefully considered to ensure that the curve stays continuous. Example:Let's take an example of stepbystep Hilbert Curve point generation and presentation in C: Output: Enter the order of Hilbert Curve: 3 Points on the Hilbert Curve: (7, 0) (6, 1) (7, 1) (7, 1) (5, 2) (4, 3) (5, 3) (5, 1) (6, 2) (5, 3) (6, 3) (6, 1) (5, 1) (6, 2) (5, 2) (5, 0) (3, 4) (2, 5) (3, 5) (3, 3) (1, 6) (0, 7) (1, 7) (1, 5) (2, 6) (1, 7) (2, 7) (2, 5) (1, 3) (2, 2) (1, 2) (1, 4) (4, 4) (3, 5) (4, 5) (4, 3) (2, 6) (1, 7) (2, 7) (2, 5) (3, 6) (2, 7) (3, 7) (3, 5) (2, 3) (3, 2) (2, 2) (2, 4) (1, 1) (2, 2) (1, 2) (1, 0) (3, 3) (4, 4) (3, 4) (3, 2) (2, 3) (3, 4) (2, 4) (2, 2) (3, 0) (2, 1) (3, 1) (3, 1) Explanation:1. Header File Inclusions: The code starts by incorporating the required header files, including "stdio.h" for common input and output functions and "math.h" for mathematical operations like "pow()". 2. The hilbertCurve Function: This function uses recursion to produce the Hilbert Curve's points. There are numerous parameters:
3. Base Case: When n decreases to 0, it is the recursion's default scenario. Here, the function outputs the current location (x, y) as a point on the curve. 4. Recursive Steps: The function uses four recursive calls for each level of recursion to represent the four quadrants of the current square. The position (x, y) and direction vectors are updated by these calls based on the quadrant and recursion level that are currently in use.
5. main Function: The user is invited to enter the Hilbert Curve's order (n) in the main() function.
In this C program, the Hilbert Curve concept is illustrated via recursion. By the usersupplied order, the hilbertCurve function recursively divides a square to produce points on the curve. The application is an excellent illustration of how recursive algorithms may be utilized to produce intricate geometric patterns.
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