hi
i wanna share some math part here i use in Shader - or code they help me for create some short and useful code
they are tested and always work so you can use them without you wanna understand the inner code algorithm
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negative or positive
if(x>0) return 1 else return -1;
(x > 0. ? 1. : -1)
or
( x / (abs(x) + 0.00001) )
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circle path
position.x = sin(time)*circle_radius;
position.z = cos(time)*circle_radius;
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rounded sguare
var a = Math.sin(i3.14159265/180.);
var b = Math.cos(i3.14159265/180.);
sphere.position.x = ( a / ( Math.abs(a) + 0.0001) ) * ( Math.pow(Math.abs(a),0.5))*3.;
sphere.position.z = ( b / ( Math.abs(b) + 0.0001) ) * ( Math.pow(Math.abs(b),0.5))*3.;
https://www.babylonjs-playground.com/#ZNQP8G#2
https://www.babylonjs-playground.com/#ZNQP8G#3
4 Likes
exact square edge path
var sq_seg = 100; // any edge segments
var p = {x:0.,y:0.,z:0.};
var i1 =time+sq_seg-1 ;
var i2 = Math.floor(i1/sq_seg);
var i3 = sq_seg- i1%sq_seg;
var i31 = 1.-(i3-1)*(1./sq_seg);
var i4 = 1.- 1./sq_seg*(i1%sq_seg)-1./sq_seg;
if(i2==0 ) p = {x:0.,y:0,z:0};
if(i2==1 ) p = {x:i31,y:0,z:0};
if(i2==2 ) p = {x:1 ,y:0,z:i31};
if(i2==3 ) p = {x:i4,y:0,z:1};
if(i2==4 ) p = {x:0,y:0.,z:1.*i4};
p.x -= 0.5;
p.z -= 0.5;
p.x *= edge_length;
p.z *= edge_length;
https://www.babylonjs-playground.com/#ZNQP8G#4
https://www.babylonjs-playground.com/#ZNQP8G#5
https://www.babylonjs-playground.com/#ZNQP8G#7
5 Likes
Why not rely on sign : sign - OpenGL 4 Reference Pages ?
I usually try the (x-xc) ^ 2 + (y-yc) ^ 2 - radius ^ 2 == 0 to prevent the expensive sin and cos when I can
For some others amazing ones: Inigo Quilez :: computer graphics, mathematics, shaders, fractals, demoscene and more
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are you scared about this 2 beauty ( sin, cos ) ?
not scared but if it can be replaced by 2 add and mul, I dunno I am trying to keep it there 
But agree it is a heavily premature optim
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i know you wanna help to me to continue some more math helpers
same as dance challenge on stage
3 Likes
the important math key
keep your base numbers between 0 - 1
you can do anything on the result
for example if you have the x between 0-1 you can use pow function and the result always stay in that range too
https://www.babylonjs-playground.com/#ZNQP8G#11
https://www.babylonjs-playground.com/#ZNQP8G#12
2 Likes
the important stuff is you make it understandable
The geometryBuilder code use them i stat make them object oriented math function
i next few days i show how can detect wall without raycast only by matematical
2020-07-12-21-38-11
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2 way for scale a big number between 0 - 1
- use y = 1.- ( a / ( x-a ));
it is start from 0 and never meet 1
a is the fixed number for control result scaling speed
https://www.babylonjs-playground.com/#ZNQP8G#18
2 . use y = log(x+1) / log(max+1.);
it is start from 0 and meet 1
max is the maximum x number you have
how can correct math frequency for “cos” function
problem : when we use math in shader we call any function for each pixel so GPU dont understand any before and after so for example when we use “Cos( x * y )”
that work fine in the small area
but that not work well in “Cos(xy100)”
nomaly that make a lot noise
you can use smoothStep function and mixing some other cos value for fix that
hey again
[Prime numbers] ( you can use binary too but this is faster )
if you wanna use multiple condition(boolean) in one integer number that is best and fast way
you can use 16 flag in one long integer (recommended for add flags uniform to shader)
// index: 0 ,1, 2 ,3, 4 ,5 ,6 ,7 ,8 ,9 , 10 , 11,12 ,13 ,14 ,15
// prim = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 , 53];
var a = 1; // all flag is down
a =2*3; // 2 flag is up
if(a%2 == 0) // check flag 0
if(a%3 == 0) // check flag 1
if(a%(2 * 3 * 7 * 11) == 0) // check flag 0,1,3,4 in same time
if(a == 1) // check all flag off
// shader mode
if( mod(a,2) == 0 ) // check flag 0
a/= 3; // remove flag from list ::))))
1 Like
Could you share the code for this? 
hey @samevision sorry for late
here is code for detect close point an the wall ( inside is allowed )
https://www.babylonjs-playground.com/#Z2TXI0#2 ( inside and outside is allowed )
performance test : 400 check wall in same time
you can detect a wall direction too
https://www.babylonjs-playground.com/#Z2TXI0#5 ( inside and outside is allowed )
under constriction
3 Likes
one of the most important ones
linear interpolation
lerp(a, b, n) => (1 - n) * a + n * b;
for example - move an object or camera alpha/beta/radius smoothly
val = lerp(val, targetVal, speed);
3 Likes