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Example: Parabolic Vault Height Calculator (Hardcoded) in C
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// 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; }
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