Rounded Polygon Node

Description

Generates a rounded polygon shape based on input UV at the size specified by inputs Width and Height. The input Sides specifies the number of sides, and the input Roundness defines the roundness of each corner.

You can connect a Tiling And Offset Node to offset or tile the shape. To preserve the ability to offset the shape within the UV space, the shape does not automatically repeat if you tile it. To achieve a repeating rounded polygon effect, first connect your UV input through a Fraction Node.

You can only use the Rounded Polygon Node in the Fragment Shader Stage.

Ports

Name	Direction	Type	Binding	Description
UV	Input	Vector 2	UV	Input UV value
Width	Input	Float	None	Rounded Polygon width
Height	Input	Float	None	Rounded Polygon height
Sides	Input	Float	None	Number of sides of the polygon
Roundness	Input	Float	None	Roundness of corners
Out	Output	Float	None	Output value

Generated Code Example

The following example code represents one possible outcome of this node.

void RoundedPolygon_Func_float(float2 UV, float Width, float Height, float Sides, float Roundness, out float Out)
{
    UV = UV * 2. + float2(-1.,-1.);
    float epsilon = 1e-6;
    UV.x = UV.x / ( Width + (Width==0)*epsilon);
    UV.y = UV.y / ( Height + (Height==0)*epsilon);
    Roundness = clamp(Roundness, 1e-6, 1.);
    float i_sides = floor( abs( Sides ) );
    float fullAngle = 2. * PI / i_sides;
    float halfAngle = fullAngle / 2.;
    float opositeAngle = HALF_PI - halfAngle;
    float diagonal = 1. / cos( halfAngle );
    // Chamfer values
    float chamferAngle = Roundness * halfAngle; // Angle taken by the chamfer
    float remainingAngle = halfAngle - chamferAngle; // Angle that remains
    float ratio = tan(remainingAngle) / tan(halfAngle); // This is the ratio between the length of the polygon's triangle and the distance of the chamfer center to the polygon center
    // Center of the chamfer arc
    float2 chamferCenter = float2(
        cos(halfAngle) ,
        sin(halfAngle)
    )* ratio * diagonal;
    // starting of the chamfer arc
    float2 chamferOrigin = float2(
        1.,
        tan(remainingAngle)
    );
    // Using Al Kashi algebra, we determine:
    // The distance distance of the center of the chamfer to the center of the polygon (side A)
    float distA = length(chamferCenter);
    // The radius of the chamfer (side B)
    float distB = 1. - chamferCenter.x;
    // The refence length of side C, which is the distance to the chamfer start
    float distCref = length(chamferOrigin);
    // This will rescale the chamfered polygon to fit the uv space
    // diagonal = length(chamferCenter) + distB;
    float uvScale = diagonal;
    UV *= uvScale;
    float2 polaruv = float2 (
        atan2( UV.y, UV.x ),
        length(UV)
    );
    polaruv.x += HALF_PI + 2*PI;
    polaruv.x = fmod( polaruv.x + halfAngle, fullAngle );
    polaruv.x = abs(polaruv.x - halfAngle);
    UV = float2( cos(polaruv.x), sin(polaruv.x) ) * polaruv.y;
    // Calculate the angle needed for the Al Kashi algebra
    float angleRatio = 1. - (polaruv.x-remainingAngle) / chamferAngle;
    // Calculate the distance of the polygon center to the chamfer extremity
    float distC = sqrt( distA*distA + distB*distB - 2.*distA*distB*cos( PI - halfAngle * angleRatio ) );
    Out = UV.x;
    float chamferZone = ( halfAngle - polaruv.x ) < chamferAngle;
    Out = lerp( UV.x, polaruv.y / distC, chamferZone );
    // Output this to have the shape mask instead of the distance field
    Out = saturate((1 - Out) / fwidth(Out));
}