Example: Generic Parabolic Vault Height Calculator (User Input) in C

// Generic Parabolic Vault Height Calculator (User Input)
#include <stdio.h>
#include <math.h> // Not strictly needed for vertex calc but good practice for math functions

// Function to calculate the y-coordinate of a parabolic vault
// y = k * x * (x - span), where k = -4 * rise / (span^2)
double getParabolicY(double x, double span, double target_rise) {
    double k = -4.0 * target_rise / (span * span);
    return k * x * (x - span);
}

int main() {
    // Step 1: Declare variables for vault parameters
    double user_span;
    double user_target_rise; // This is the 'rise' we are aiming for in the equation

    // Step 2: Prompt user for vault span and desired rise
    printf("--- Generic Parabolic Vault ---\n");
    printf("Enter the total span of the vault (e.g., 12.0): ");
    scanf("%lf", &user_span);

    printf("Enter the desired maximum height (rise) of the vault (e.g., 6.0): ");
    scanf("%lf", &user_target_rise);

    // Basic validation
    if (user_span <= 0 || user_target_rise <= 0) {
        printf("Span and rise must be positive values.\n");
        return 1; // Indicate an error
    }

    // Step 3: Calculate the maximum height based on the user-defined function
    // For a symmetric parabola, the maximum height is at the midpoint of the span.
    double x_peak = user_span / 2.0;
    double actual_calculated_rise = getParabolicY(x_peak, user_span, user_target_rise);

    // Step 4: Print the calculated height
    printf("\nVault Details:\n");
    printf("  Span: %.2f units\n", user_span);
    printf("  Desired Rise: %.2f units\n", user_target_rise);
    printf("  Calculated Maximum Height (Actual Rise): %.2f units\n", actual_calculated_rise);

    return 0;
}