Math for Blending Numbers: Find "X

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In summary, the conversation discusses finding a mathematical way to blend between two numbers in an inverse square manner. It is mentioned that for a parabola, three points are needed for accuracy, but with only two points, there can be multiple solutions. The conversation also mentions using a linear blend with a power function and suggests using a uniform emission for the light source. However, it is noted that just knowing the intensity at two points is not enough information.
  • #1
fifthFunction
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TL;DR Summary
blend 2 numbers by inverse square
i have not clue if this is the right place to ask
if i had 2 numbers and i wanted to blend between them but instead of a linear way it was in an inverse square way.. how would that math go?
so if i had A=1 and B=9 and wanted the number at 0.5 it would be 4.. or if i wanted the number at 0.85 it would be "X"
 
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  • #2
It depends on what exactly you need. For a parabola you need three points (or some other additional information), with just two points it is ambiguous.

As an example, f(x)=(2x+1)2 satisfies f(0)=1 and f(1)=9 and it matches f(0.5)=4, but g(x)=(x+3.5)2-11.25 fits your two borders as well, it would give g(0.5)=4.75.

Anyway: If you want a parabola, find the equation for the parabola you want, then plug in different numbers.
 
  • #3
i think the most simple way to explain what i am trying to do is to map a section of a gradient of the falloff of light?
so say you have a strip of paper with a light at one end and you measure how bright one side is and how bright the other side is.. you input that into the function and it would tell you how bright the middle of the paper is
 
  • #4
That depends on where your light source is and how its emission looks like. For a uniform emission you get an inverse square law for the intensity, modified with the incidence angle if not orthogonal. Just knowing the intensity at both sides is not sufficient.
 
  • #5
ok so it seems if i do something like A=sqrt(1),B=sqrt(9),P=0.5 then just feed that into a linear blend pow(mix(A,B,P),2) it works.. don't know if its the best way tho
 

Related to Math for Blending Numbers: Find "X

1. What is "X" in math for blending numbers?

"X" is a variable used in algebra to represent an unknown value. It can be any number or quantity that needs to be solved for.

2. How do you find "X" in a math problem?

To find "X" in a math problem, you need to isolate it on one side of the equation by using inverse operations. This means performing the opposite operation of what is being done to "X" on both sides of the equation until "X" is left by itself.

3. What is the purpose of finding "X" in math?

The purpose of finding "X" in math is to solve for an unknown value in an equation or problem. It allows us to find the missing piece of information and understand the relationship between different quantities.

4. Can "X" have multiple values?

Yes, "X" can have multiple values depending on the given equation or problem. In some cases, there may be more than one solution for "X" that satisfies the equation.

5. How can I practice finding "X" in math problems?

You can practice finding "X" by solving various algebraic equations and word problems. There are also many online resources and textbooks that provide practice problems and solutions. Additionally, working with a tutor or attending a math class can also help improve your skills in finding "X".

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