compute()

vec2f fl::HeartPath::compute ( float alpha )

overridevirtual

Implements fl::XYPathGenerator.

Definition at line 53 of file xypath_impls.cpp.

                                    {
    // Parametric equation for a heart shape
    // α in [0,1] → (x,y) on the heart curve
    float t = alpha * 2.0f * PI;
 
    // Heart formula based on a modified cardioid with improved aesthetics
    float x = 16.0f * powf(sinf(t), 3);
 
    // Modified y formula for a more balanced heart shape
    // This creates a fuller bottom and more defined top curve
    float y = -(13.0f * cosf(t) - 5.0f * cosf(2.0f * t) -
                2.0f * cosf(3.0f * t) - cosf(4.0f * t));
 
    // Scale to fit in [-1, 1] range
    // The 16.0f divisor for x ensures x is in [-1, 1]
    x /= 16.0f;
 
    // Scale y to ensure it's in [-1, 1]
    // The 16.0f divisor ensures proper scaling while maintaining proportions
    y /= -16.0f;
 
    // Apply a slight vertical stretch to fill the [-1, 1] range better
    y *= 1.10f;
 
    y += 0.17f; // Adjust y to fit within the range of [-1, 1]
 
    return vec2f(x, y);
}

References PI, x, and y.