I am doing some programming, where I am interpolating point a to point b, against a timer that is constantly incrementing by 0.005
I am using Linear Interpolation as a technique, and from researching the internet, there are many ways of interpolating.
My senior gave me this equation, that matches the diagram;
P(t) = (1-t)*P + t*Q
I do not understand, the letters used in this equation, so I have done research and found this equation from Interpolation in 3D graphics.
Here the author of the answer uses this equation;
(max-min)
location = min + (current_step) * --------
steps
I had used this equation/algorithm in my programming exercise, and it works. In terms of mathematics, I converted the equation provided by the author in to maths;
P(x) = a +(c)*(b-a)/a
P(y) = a +(c)*(b-a)/a
OR (similar to first algorithm/equation)
P(x) = (1-c) * a + c * b
P(y) = (1-c) * a + c * b
My question is; the converted language into maths set, is that correct in terms of mathematics, and can someone explain;
P(t) = (1-t)P + tQ
I will answer your questions in order, and show how the formula from the other question really should be the same one as that which your senior gave you, and then I will explain what that equation means.
In answer to your first question, what you have there is unfortunately not correct - indeed the answerer in the Interpolation in 3D Graphics is not quite correct either.
My understanding is that you start with $2$ points $P_0=(x_0,y_0)$ and $P_1=(x_1,y_1)$. Instead of the answerer saying "min" and "max" the answerer should have said "the coordinate in the first point" and "the coordinate in the second point." The formula should be that at step number $n$ the location should be $$P_0+n\times\frac{P_1-P_0}{\text{total number of steps}}$$ However, this is just the same as the equation your senior gave you because $\frac{n}{\text{total number of steps}}$ is just the same as your $t$. which gives you $$P_0+n\times\frac{P_1-P_0}{\text{total number of steps}}=P_0+t(P_1-P_0)=(1-t)P_0+tP_1$$
Now, we can finally move on to what the equation means.
First off the equation which you are given suffers from some slightly bad notation: $$P(t)=(1-t)P+tQ$$ is bad because the $P(t)$ means the point we should get at time $t$ which is not the same variable as $P$ which means the point $P_0$. Let me instead give you the same equation with slightly better notation and using the variables $P_0$ and $P_1$ you defined in the picture:
$$P(t)=(1-t)P_0+tP_1$$
Here plugging in a $t$ gives you the point you should get for time $t$ while $P_0$ is the first point and $P_1$ is the last point. You may notice and be confused by the fact that we are multiplying a point by a number, but this is really shorthand for multiplying both coordinates by that number - meaning we have $$\begin{align}P(t)&=(1-t)P_0+tP_1\\&=((1-t)x_0,(1-t)y_0)+(tx_1,ty_1)\\&=((1-t)x_0+tx_1,(1-t)y_0+ty_1)\end{align}$$
In other words the $x$-coordinate at time $t$ should be $$(1-t)x_0+tx_1$$ while the $y$-coordinate at time $t$ should be $$(1-t)y_0+ty_1$$
Notice how plugging in $t=0$ gives you $(x_0,y_0)$ and plugging in $t=1$ gives you $(x_1,y_1)$ as desired.