What is the mathematical formula behind the Env object? more specificaly how is "curve" derived mathematicaly?

eskay · June 4, 2022, 10:28am

Hello everyone!

I need to underastand how the Env object draws the shape of the envelope in order to use it in a project that I am working on.

Env.new(levels: [0, 1, 0.9, 0], times: [0.1, 0.5, 1], curve: [-5, 0, -5]).plot;

the levels and times are self explanatory, but what about Curve?
Obviously it describes curvature, but according to what? is it somehow derived from the tangent line at that point, is it the best approximating circle that passes through that point and use its reciprocal radius to describe it? what is the formula behind it? I need to know because lets say I would like to reconstruct the same line in a different program that uses a different logic to construct lines… Basically how is “curve” derived?

any insight would be highly appreciated!

thank you

scztt · June 4, 2022, 10:42am

You can find the equation for curve in the lincurve method. This should match the implementations in other places like envelopes / on the server.

github.com

supercollider/supercollider/blob/8c87fbeb6db6eead38bfd77a0789f2e9b6a6f8ec/SCClassLibrary/Common/Math/SimpleNumber.sc#L449

      
        
            			\min, {
            				if(this <= inMin) { ^outMin };
            			},
            			\max, {
            				if(this >= inMax) { ^outMax };
            			}
            		);
            		^pow(outMax / outMin, log(this / inMin) / log(inMax / inMin)) * outMin
            	}
            
            
	lincurve { |inMin = 0, inMax = 1, outMin = 0, outMax = 1, curve = -4, clip = \minmax|
            		var grow, a, b, scaled;
            		switch(clip,
            			\minmax, {
            				if(this <= inMin) { ^outMin };
            				if(this >= inMax) { ^outMax };
            			},
            			\min, {
            				if(this <= inMin) { ^outMin };
            			},
            			\max, {

dkmayer · July 8, 2022, 9:18pm

Hi, maybe this helps: