Hallo,

before I ask my question, I shell say that my math knowledge and subsequently my logical thinking is very poor.

I have a sphere. this sphere spins with a certain speed. When the speed gets higher, the sphere should "get hotter" and therefor more red. When slowing down, it "cools down" and gets more blueish.

so how do I relate the color with speed?

green = speed*pointSize/255); // smaller points get darker
red = green + abs(sin(speed)*255/pointSize;
blue = green - abs(sin(speed)*255/pointSize;

I have no idea how to solve this problem mathematically.    

Thanks for any help!  

I found it very useful to change the colormode from RGB to HSB (Hue Saturation Brightness) and then only vary the H value in the interval red-yellow.

it doesnt work like that.
there is no hue value for red+yellow or any other color.
hue is the color.
so when defining a color that should be between red and yellow use hue values between 0 and 60

this only works because red and yellow are next to each other, to get frmo red to green without yellow for example, you should use lerpcolor again.

so in your case you can use,

color(map(speed,0,maxSpeed,0,60),100,100);
when in HSB Mode.

kein grund zu verzweifeln. can you post a part of your code, i will make it work

Thats just a selection of the application that I use to test the functions on.

Now I`m struggling with the color-change and the rotation in a determined number of cycles, in which the speed decreases/increases to min/max speed.

Code:

float rotation;
float speed, speedMin, speedMax,speedAvrg;
int cycles;
float radius;
int wRings, hRings;
float angle;

void setup()
{
  size(400,400);
  colorMode(RGB);
  background(0);

  radius  = height/2;
  wRings = 30;
  hRings = 30;

  cycles = 10;
  speedMin = 0;
  speedMax = 0.1;
  speedAvrg = 0.05;

  speed = 0.001;

}


void draw()
{
  noStroke();
  fill(0,40);
  rect(0,0,width,height);
  drawSphere();
  rotateSphere();
}


void drawSphere()
{ 
  float posx = mouseX;
  float posy = mouseY;

  for(int i=1; i<wRings; i++)
  {
    float phase = i*1./wRings;
    float ringCenterPosX = posx;
    float ringCenterPosY = posy + (sin(phase*PI+HALF_PI)*.5+.5)*radius-height/4;
    float ringSizeX = sin(phase*PI)*radius/2;
    float ringSizeY = ringSizeX / 4;

    drawRing(ringCenterPosX, ringCenterPosY, ringSizeX, ringSizeY);
  }

}

void drawRing(float posx, float posy, float sizex, float sizey)
{
  
  for(int i=0; i<hRings;i++)
  {
    float phase = i*.4/hRings - rotation;

    //    color red = #ff0000;
    //    color blue = #0000ff;
    //    float colorPercent = sin(speed*100)*100;     
    //    fill(lerpColor(blue, red, colorPercent, HSB));    

    //    c =  color(abs(sin((speed))*255)/pointSize, 255-abs(cos((speed))*255)/pointSize, 255.0/(speed));
    //    color c = color(map(speed,0,speedMax,0,60),0,0);
    
    float colorShifter = sin(speed*100);
    float cRed = 255*colorShifter;
    float cBlue = 255-255*colorShifter;
    //  println("RED: " + cRed + "BLUE: " + cBlue);
    fill(cRed,255,cBlue);  

    float pointSize = abs(sin(phase+rotation)*TWO_PI);
    ellipse(posx + sizex*cos(phase*TWO_PI), posy + sizey*sin(phase*TWO_PI),pointSize,pointSize);
  }
  rotation += speed;
}


void rotateSphere(float speed, int cycles)
{
  for(int i=0;i<cycles+1;i++)
  {
    float difference = speed*i/cycles;  // DECREASING SPEED to SPEEDMIN
    //float difference = (speedMax-speed)*i/cycles;  //INCREASING SPEED TO SPEEDMAX

    for(int j=0; j<360; j++)
    {

	speed -= difference/360;
	rotation -=speed;
	println("CYCLE: " + i + "| GRAD: " + j + " @ SPEED: " + speed);     
    }
  }
}

float count = 0;

void rotateSphere()
{ 
  for(int j=0;j<10;j++){

    for(int i=0; i<360; i++)
    { 
	count = (count%1)+0.1;
	float phase = sin(count)*TWO_PI;
	angle = (angle+degrees(phase));
    }
  }
}
 

It`s messy, but thats my  'draft' where I can experiment, without ruining my main app.

Ich hoff du kannst da durchblicken  

well I`ve been trying to make a function, that spins the sphere a certain number of times (n*360) and while spinning loose or gain speed.

void rotateSphere(float speed, int cycles)
{
 for(int i=0;i<cycles+1;i++)
 {
   float difference = speed*i/cycles;  // DECREASING SPEED to SPEEDMIN
   //float difference = (speedMax-speed)*i/cycles;  //INCREASING SPEED TO SPEEDMAX

   for(int j=0; j<360; j++)
   {

     speed -= difference/360;
     rotation -=speed;
     println("CYCLE: " + i + "| GRAD: " + j + " @ SPEED: " + speed);    
   }
 }
}

If the speed, at which the sphere is 'born' is under the average speed, it gets accelerated to speedMax; and vice verca.  When accelerating, the temperature gets higher, hence the color > red. And vice verca.

In this code there is no function that creates a sphere using the constructor. I just adjust the numbers manually to see what happens whit the color and so on.

The code for my main app is to long to post in here...

i like it
some color change is somehow tricky, cause lerpcolor gives you just a two color gradient, and the HSB idea only works going from red,yellow,green to blue...

if you want a gradient from blue to red, orange, yellow, white maybe. you have to think about different ways.

but hope that helps.

Code:

float rotation;
float speed;

float radius;
int wRings, hRings;
float angle;

void setup()
{
  size(400,400);
   colorMode(HSB,360,100,100);
  background(0);

  radius  = height/2;
  wRings = 30;
  hRings = 30;

}


void draw()
{
  noStroke();
  fill(0,40);
  rect(0,0,width,height);
  drawSphere();
  rotateSphere();

}


void drawSphere()
{ 
  float posx = mouseX;
  float posy = mouseY;

  for(int i=1; i<wRings; i++)
  {
    float phase = i*1./wRings;
    float ringCenterPosX = posx;
    float ringCenterPosY = posy + (sin(phase*PI+HALF_PI)*.5+.5)*radius-height/4;
    float ringSizeX = sin(phase*PI)*radius/2;
    float ringSizeY = ringSizeX / 4;

    drawRing(ringCenterPosX, ringCenterPosY, ringSizeX, ringSizeY);
  }

}

void drawRing(float posx, float posy, float sizex, float sizey)
{

  for(int i=0; i<hRings;i++)
  {
    float phase = i*.4/hRings - rotation;

    fill(180-(180*speed*100),100,100);
   
    float pointSize = abs(sin(phase+rotation)*TWO_PI);
    ellipse(posx + sizex*cos(phase*TWO_PI), posy + sizey*sin(phase*TWO_PI),pointSize,pointSize);
  }
  rotation -= speed;

  speed=map(sin(frameCount/100.0),-1,1,0,0.01);

}


float count = 0;

void rotateSphere()
{  
  for(int j=0;j<10;j++){

    for(int i=0; i<360; i++)
    { 
	count = (count%1)+0.1;
	float phase = sin(count)*TWO_PI;
	angle = (angle+degrees(phase));
    }
  }
}



 

if you ad this line to your drawRing function

   hRings = (int) map(speed,0,0.01,2,40);

it looks more realistic as the trail get shorter when slowing down.
Not perfect but you get the idea.