2d game geometry

[andrewjb123]

I have the following problem:



I have asked the same question here: http://math.stackexchange.com/quest...s/2089369?noredirect=1#comment4294547_2089369

and have used the formula given to work out 8 and it is the correct value. But im really struggling to understand how each part of the formula was worked out.

ideally what i want is to be able to plug in the value of 2 height 2, 15 height 5 - and give an index of 8 (or other) which will give me the corresponding height.

 

[stapel]

I have asked the same question here: http://math.stackexchange.com/quest...s/2089369?noredirect=1#comment4294547_2089369

and have used the formula given to work out 8 and it is the correct value. But im really struggling to understand how each part of the formula was worked out.

Which part is confusing to you? Please be specific. Thank you!

 

[andrewjb123]

Which part is confusing to you? Please be specific. Thank you!

well, I’ve been reading here how to work out the equation of a straight line,


http://mathonweb.com/help_ebook/html/graphs_2.htm


and looked at these particular sentence


Find any two points, (x₁, y₁) and (x₂, y₂), on the line and substitute their coordinates into the following formula to get m:


this is easy because i know what x1, y1 and x2, y2 are as values, so i can find m easily.


then it comes to calculating b, and i can’t see how on earth i can calculate b, it says:

• Get b from inspection of the y intercept of the graph.

well how can i do this in an equation without having to visually see the y intercept on a graph as show in the graph in their example, i can visually see it, but i want to be able to calculate it as i want to create a function in code which i can plug in the values (any values not just the ones in my example) so i can calculate depth in a 2d scene? is it possible?


I think (and correct me if I’m wrong) but this is how he got + 20 ? (+ 20 is + b)

 

[andrewjb123]

h = 3/13i - 6/13 + 26/13

in this part of the equation how is 26/13 found? I can see that 26/13 = 2 - but what if i dont know that 20+6 / 13 = 2 ? how would i get the 20 part?

 

[andrewjb123]

think i have nailed it

var h1 = 2;
var i1 = 2;
var h2 = 5;
var i2 = 15;
var i = 8;
var calc1 = h2 - h1; // 3
var calc2 = i2 - i1; // 13
var calc3 = calc2 * h2; // 13*5=65
var calc4 = calc1 * i2; // 45
var calc5 = calc3 - calc4; // 20
var calc6 = ((calc1 * i) + calc5) / calc2;