Procedural modeling.



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This is the starting of the series on procedural modelling. it helps to create procedural models in unity.


This tutorial is made with Unity 2020.3.7f1.


1. Bezier curve in unity


We begin by introducing the Bezier curve in unity, the concepts, and the underlying mathematics behind the curve. let me start with linearly interpolating between two points unity using lerp function.


Vector3 result =Vector3.Lerp(green, red, t);


Interpolation of white ball between red and

green ball based on t value

(value of result will be green if t=0, red when t=1.).


If we lerp between two lerped results we get a quadratic lerp.


 Vector3 QuadraticLerp(Vector3 a, Vector3 b, Vector3 c, float t)
 {
   lerp1= Vector3.Lerp(a, b, t);
   lerp2 = Vector3.Lerp(b, c, t);
   return Vector3.Lerp(lerp1, lerp2, t)
 }

Quadratic lerp


Now if we lerp again between two quadratic lerped values we get a cubic lerp.


 Vector3 CubicLerp(Vector3 a,Vector3 b,Vector3 c,Vector3 d,float t)
 {
   Vector3 lerp1=QuadraticLerp(a, b, c, t);
   Vector3 lerp2= QuadraticLerp(b, c, d, t); 
   return Vector3.Lerp(lerp1, lerp2, t);
 }
 

cubic lerp

If we join plot the trajectory of the blue ball we get a cubic bezier curve. first and the last point(green) are called anchors and the middle two points(green) are handles.

we can draw a cubic bezier curve using DrawBezier function in unity.


Handles.DrawBezier(a, b, c,d, Color.green,null,2f);


Bezier curve in unity.

We will explore more on unity bezier curve and its implementation to create procedurally generated roads in unity in upcoming sections.


So until then bye.


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