I'm having hard times transforming a math formula to code. I can solve it on the paper easily, but it's hard for me to bring it into code form. Is it generally possible to bring a math formula directly into a program, or, if not, how can it be transferred?
Taking, for example, the Pythagorean Theorem:
a² + b² = c². Having
b defined in the code, it is straight forward to apply this formula.
c = sqrt(pow(a, 2) + pow(b, 2))
Currently, I'm having hard times bringing the line-line intersection, that I've solved on paper, into my program. Assuming a line being defined as
L: O + a * D, one can find the intersection of two lines by setting them as equal.
L1: O1 + a * D1 L2: O2 + b * D2 => O1 + a * D1 = O2 + b * D2
Using pen an paper, I would have already defined values and can solve the equation by splitting the equation into three sub-equations and applying simple substituion (I hope you can read my hand writing):
My actual problem
... is that substitution can not be applied algorithmically, or I don't know how to do. The equation
L1 = L2 must be transformed to a generalized formula that can be directly translated into code (like
a² + b² = c²), but I don't know how.
I was hoping for a step-by-step explanation (either as answer or linked) on how to come to the formula/algorithm I am searching for. I know there are quite many websites that describe the intersection of two lines, but I would like to understand how to find the algorithm from a mathematical starting point.