Example: Parabolic Vault Height Calculator (Hardcoded) in C

// Parabolic Vault Height Calculator (Hardcoded)
#include <stdio.h>
#include <math.h> // For fmax, though not strictly needed for vertex calculation

// Function to calculate the y-coordinate of a parabolic vault
// Assuming a vault centered at x = span/2, opening downwards.
// The equation y = k * x * (x - span) has y=0 at x=0 and x=span.
// Max height 'rise' occurs at x=span/2.
// Substituting, rise = k * (span/2) * (span/2 - span) = k * (span/2) * (-span/2) = -k * span^2 / 4
// So, k = -4 * rise / (span^2)
double calculateParabolicY(double x, double span, double derived_rise) {
    double k = -4.0 * derived_rise / (span * span);
    return k * x * (x - span);
}

int main() {
    // Step 1: Define vault parameters (hardcoded for this example)
    double span = 10.0; // Total width of the vault
    double derived_rise = 5.0; // The rise used to derive the parabolic equation

    // Step 2: Calculate the maximum height (rise) of the vault
    // For a symmetric parabola defined as above, the maximum height is at the midpoint of the span.
    double x_at_max_height = span / 2.0;
    double actual_max_height = calculateParabolicY(x_at_max_height, span, derived_rise);

    // Step 3: Print the calculated height
    printf("--- Hardcoded Parabolic Vault ---\n");
    printf("Vault Span: %.2f units\n", span);
    printf("Calculated Maximum Height (Rise): %.2f units\n", actual_max_height);

    return 0;
}