More Features
mattdesl opened this issue · comments
The guide is not complete. More planned features:
- cross product
- tensor product
- delta
- dot product
common patterns like clamped dot product with angled bracketstoo specific I think
- indefinite integral
- ƒ - function
-
Heaviside function (possibly too specific; already have sgnstep()) - common patterns like greek letters vs latin ?
And generally:
- converting some complex/intimidating expressions into code
- notation-to-code examples from real papers (e.g. graphics programming papers)
I didn't want to open a new issue. Instead, I'm adding here:
- Smoothstep and clamp
function clamp(a,b,c){
return Math.max(b,Math.min(c,a));
}
function smoothstep(edge0, edge1, x)
{
// Scale, bias and saturate x to 0..1 range
x = clamp((x - edge0)/(edge1 - edge0), 0.0, 1.0);
// Evaluate polynomial
return x*x*(3 - 2*x);
}- Angle conversions e.g. degree to radian
// Converts from degrees to radians.
Math.radians = function(degrees) {
return degrees * Math.PI / 180;
};
// Converts from radians to degrees.
Math.degrees = function(radians) {
return radians * 180 / Math.PI;
};- Spherical to cartesian etc
function sph2cart(vect) {
//r, theta, phi
var z = vect.x * Math.sin(vect.z);
var rcoselev = vect.x * Math.cos(vect.z);
var x = rcoselev * Math.cos(vect.y);
var y = rcoselev * Math.sin(vect.y);
return new THREE.Vector3(x, y, z);
}
};
This is a super cool project.
Something that baffled me when first reading FP literature was the frequent use of "prime" notation: e.g. an equation that contained both a and a' and sometimes even a''. It took me a while just to figure out what this was called.
Also, in general I have trouble grokking something if I can't "read it aloud" in my head. So any guidance for how to say notation is greatly helpful for people like me.
@cihadturhan cheers, I will consider those. I eventually hope to have another part of the repo that holds "practical examples" (aimed at graphics programming), and it might include turning equations into, say, GLSL built-ins like sign, step and smoothstep.
@avdi thanks for the feedback. See #5 which includes prime 😄
Dunno if this might interest you, but I found this website the other day: http://visualgo.net/ and the way they present their explanations is makes it seem really simple to understand (though they could use a bit less pseudocode IMHO)
Here's a huge list of math symbols:
https://en.wikipedia.org/wiki/List_of_mathematical_symbols
i would like to see matrix algebra features like transpose, complex conjugate, etc.. as matrices are real big deal :) and don't forget there are also other algebras than Gibbs (Clifford, etc)...
this is excellent - thanks!
i think it would be really helpful to see example (simple) implementations of the functions mentioned, such as dot, cross and determinant
I like the project a lot. I especially like the idea of focusing on mathematical operators (which are easy to write but can be pretty involved to compute) and not whole algorithms because there are plenty of books describing algorithms. I always think of mathematical operators as small programs and if I don't have a corresponding program in my head I don't really understand the operator. Having had a guide like yours would have saved me a ton of time when I was younger.
I would love to see a "numerical math" section which presents operators such as integrals, derivatives, gradients and laplacians etc. because using numerics is how most of these things are implemented in practice (and it's often easier to understand I think)
As examples: given are the values of a function f(x) at discrete points in the form of an array.
- The derivative f'(p) at grid point p is just the difference of its neighbors f'(p) = f(p+1)-f(p).
- A laplacian is somewhat similar the average of all the differences between the surrounding points in n dimensions.
- An integral is just the sum of the values which shows the similarity in the used signs: a large cursive S for integral sums and a large Greek Sigma for the summation operator.
@chmaruni Thanks for the feedback. Things with limits (derivatives, integrals, infinity) are going to be tough to translate into code. Discrete points might work for certain things... The same is done here and makes sense to me. 😄
I agree, operators with limits, infinites and infinitesimals sometimes seem borderline magic and hard to grasp. That's why I think that seeing how they operate on discrete functions (aka arrays) is so helpful, because more often than not they are pretty trivial things with fancy names.
@mattdesl interesting video. He is still solving the integral analytically however (ie using transformation rules to get rid of the integrals) which is not exactly what I meant but still interesting of course. If you have the values of the function on an evenly spaced grid you can for example usd the trapezoidal rule, see "numerical implementation" here: https://en.m.wikipedia.org/wiki/Trapezoidal_rule
I would love to see a "numerical math" section which presents operators such as integrals, derivatives, gradients and laplacians etc.
I would love too.
Things with limits (derivatives, integrals, infinity) are going to be tough to translate into code.
Exactly because they're tough to translate it's necessary to show even a few examples to give people idea how they can understand it.
I agree, operators with limits, infinites and infinitesimals sometimes seem borderline magic and hard to grasp. That's why I think that seeing how they operate on discrete functions (aka arrays) is so helpful, because more often than not they are pretty trivial things with fancy names.
Totally agree!
Can be cool if you create a branch with mathematical formulas that we use in Machine Learn ( Gini, entropy, gain, similarity, euclidian distance ... ) ^ - ^
What do you mean delta, the laplacian or?
This is what I am looking for :)
Here are my suggestions:
- add matlab/octave, python examples as they are more used by scientists.
- add computation geometry and image processing notations.
Mixed fractions such as
