Mathfx

From Unify Community Wiki
Revision as of 07:39, 23 October 2010 by NCarter (Talk | contribs)

Jump to: navigation, search

Contents

Description

The following snippet provides short functions for floating point numbers. See the usage section for individualized information.

Usage

  • Hermite - This method will interpolate while easing in and out at the limits.
Graph of the Hermite function.
  • Sinerp - Short for 'sinusoidal interpolation', this method will interpolate while easing around the end, when value is near one.
Graph of the Sinerp function.
  • Coserp - Similar to Sinerp, except it eases in, when value is near zero, instead of easing out (and uses cosine instead of sine).
  • Berp - Short for 'boing-like interpolation', this method will first overshoot, then waver back and forth around the end value before coming to a rest.
Graph of the Berp function.
  • Bounce - Returns a value between 0 and 1 that can be used to easily make bouncing GUI items (a la OS X's Dock)
Graph of the Bounce function.
  • SmoothStep - Works like Lerp, but has ease-in and ease-out of the values.
  • Lerp - Short for 'linearly interpolate', this method is equivalent to Unity's Mathf.Lerp, included for comparison.
Graph of the Lerp function.
  • NearestPoint - Will return the nearest point on a line to a point. Useful for making an object follow a track.
  • NearestPointStrict - Works like NearestPoint except the end of the line is clamped.

History

  • Added Approx function for testing float value within an offset range. All thanks to Opless for this!
  • Clerp added by Jeff Craighead 10:51, 2 May 2008 (PDT)
  • Added JavaScript conversion

C# - Mathfx.cs

<csharp> using UnityEngine; using System;

public class Mathfx {

   public static float Hermite(float start, float end, float value)
   {
       return Mathf.Lerp(start, end, value * value * (3.0f - 2.0f * value));
   }
   
   public static float Sinerp(float start, float end, float value)
   {
       return Mathf.Lerp(start, end, Mathf.Sin(value * Mathf.PI * 0.5f));
   }
   public static float Coserp(float start, float end, float value)
   {
       return Mathf.Lerp(start, end, 1.0f - Mathf.Cos(value * Mathf.PI * 0.5f));
   }

   public static float Berp(float start, float end, float value)
   {
       value = Mathf.Clamp01(value);
       value = (Mathf.Sin(value * Mathf.PI * (0.2f + 2.5f * value * value * value)) * Mathf.Pow(1f - value, 2.2f) + value) * (1f + (1.2f * (1f - value)));
       return start + (end - start) * value;
   }
   
   public static float SmoothStep (float x, float min, float max) 
   {
       x = Mathf.Clamp (x, min, max);
       float v1 = (x-min)/(max-min);
       float v2 = (x-min)/(max-min);
       return -2*v1 * v1 *v1 + 3*v2 * v2;
   }

   public static float Lerp(float start, float end, float value)
   {
       return ((1.0f - value) * start) + (value * end);
   }

   public static Vector3 NearestPoint(Vector3 lineStart, Vector3 lineEnd, Vector3 point)
   {
       Vector3 lineDirection = Vector3.Normalize(lineEnd-lineStart);
       float closestPoint = Vector3.Dot((point-lineStart),lineDirection)/Vector3.Dot(lineDirection,lineDirection);
       return lineStart+(closestPoint*lineDirection);
   }

   public static Vector3 NearestPointStrict(Vector3 lineStart, Vector3 lineEnd, Vector3 point)
   {
       Vector3 fullDirection = lineEnd-lineStart;
       Vector3 lineDirection = Vector3.Normalize(fullDirection);
       float closestPoint = Vector3.Dot((point-lineStart),lineDirection)/Vector3.Dot(lineDirection,lineDirection);
       return lineStart+(Mathf.Clamp(closestPoint,0.0f,Vector3.Magnitude(fullDirection))*lineDirection);
   }
   public static float Bounce(float x) {
       return Mathf.Abs(Mathf.Sin(6.28f*(x+1f)*(x+1f)) * (1f-x));
   }
   
   // test for value that is near specified float (due to floating point inprecision)
   // all thanks to Opless for this!
   public static bool Approx(float val, float about, float range) {
       return ( ( Mathf.Abs(val - about) < range) );
   }
   // test if a Vector3 is close to another Vector3 (due to floating point inprecision)
   // compares the square of the distance to the square of the range as this 
   // avoids calculating a square root which is much slower than squaring the range
   public static bool Approx(Vector3 val, Vector3 about, float range) {
       return ( (val - about).sqrMagnitude < range*range);
   }
  /*
    * CLerp - Circular Lerp - is like lerp but handles the wraparound from 0 to 360.
    * This is useful when interpolating eulerAngles and the object
    * crosses the 0/360 boundary.  The standard Lerp function causes the object
    * to rotate in the wrong direction and looks stupid. Clerp fixes that.
    */
   public static float Clerp(float start , float end, float value){
       float min = 0.0f;
       float max = 360.0f;
       float half = Mathf.Abs((max - min)/2.0f);//half the distance between min and max
       float retval = 0.0f;
       float diff = 0.0f;
       if((end - start) < -half){
           diff = ((max - start)+end)*value;

retval = start+diff;

           }
           else if((end - start) > half){
               diff = -((max - end)+start)*value;
               retval =  start+diff;
           }
           else retval =  start+(end-start)*value;
           // Debug.Log("Start: "  + start + "   End: " + end + "  Value: " + value + "  Half: " + half + "  Diff: " + diff + "  Retval: " + retval);
           return retval;
       }

} </csharp>

Js - Mathfx.js

I converted from the original C# format above. <javascript> static function Hermite(start : float, end : float, value : float) : float {

   return Mathf.Lerp(start, end, value * value * (3.0 - 2.0 * value));

}

static function Sinerp(start : float, end : float, value : float) : float {

   return Mathf.Lerp(start, end, Mathf.Sin(value * Mathf.PI * 0.5));

}

static function Coserp(start : float, end : float, value : float) : float {

   return Mathf.Lerp(start, end, 1.0 - Mathf.Cos(value * Mathf.PI * 0.5));

}

static function Berp(start : float, end : float, value : float) : float {

   value = Mathf.Clamp01(value);
   value = (Mathf.Sin(value * Mathf.PI * (0.2 + 2.5 * value * value * value)) * Mathf.Pow(1 - value, 2.2) + value) * (1 + (1.2 * (1 - value)));
   return start + (end - start) * value;

}

static function SmoothStep (x : float, min : float, max : float) : float {

   x = Mathf.Clamp (x, min, max);
   var v1 = (x-min)/(max-min);
   var v2 = (x-min)/(max-min);
   return -2*v1 * v1 *v1 + 3*v2 * v2;

}

static function Lerp(start : float, end : float, value : float) : float {

   return ((1.0 - value) * start) + (value * end);

}

static function NearestPoint(lineStart : Vector3, lineEnd : Vector3, point : Vector3) : Vector3 {

   var lineDirection = Vector3.Normalize(lineEnd-lineStart);
   var closestPoint = Vector3.Dot((point-lineStart),lineDirection)/Vector3.Dot(lineDirection,lineDirection);
   return lineStart+(closestPoint*lineDirection);

}

static function NearestPointStrict(lineStart : Vector3, lineEnd : Vector3, point : Vector3) : Vector3 {

   var fullDirection = lineEnd-lineStart;
   var lineDirection = Vector3.Normalize(fullDirection);
   var closestPoint = Vector3.Dot((point-lineStart),lineDirection)/Vector3.Dot(lineDirection,lineDirection);
   return lineStart+(Mathf.Clamp(closestPoint,0.0,Vector3.Magnitude(fullDirection))*lineDirection);

} static function Bounce(x : float) : float {

   return Mathf.Abs(Mathf.Sin(6.28*(x+1)*(x+1)) * (1-x));

}

// test for value that is near specified float (due to floating point inprecision) // all thanks to Opless for this! static function Approx(val : float, about : float, range : float) : boolean {

   return ( ( Mathf.Abs(val - about) < range) );

}

// test if a Vector3 is close to another Vector3 (due to floating point inprecision) // compares the square of the distance to the square of the range as this // avoids calculating a square root which is much slower than squaring the range static function Approx(val : Vector3, about : Vector3, range : float) : boolean {

  return ( (val - about).sqrMagnitude < range*range);

}

// CLerp - Circular Lerp - is like lerp but handles the wraparound from 0 to 360. // This is useful when interpolating eulerAngles and the object // crosses the 0/360 boundary. The standard Lerp function causes the object // to rotate in the wrong direction and looks stupid. Clerp fixes that. static function Clerp(start : float, end : float, value : float) : float {

  var min = 0.0;
  var max = 360.0;
  var half = Mathf.Abs((max - min)/2.0);//half the distance between min and max
  var retval = 0.0;
  var diff = 0.0;
  if((end - start) < -half){
      diff = ((max - start)+end)*value;
      retval =  start+diff;
  }
  else if((end - start) > half){
      diff = -((max - end)+start)*value;
      retval =  start+diff;
  }
  else retval =  start+(end-start)*value;
  // Debug.Log("Start: "  + start + "   End: " + end + "  Value: " + value + "  Half: " + half + "  Diff: " + diff + "  Retval: " + retval);
  return retval;

} </javascript>

Personal tools
Namespaces

Variants
Actions
Navigation
Extras
Toolbox