How does fWorldPerScreenWidthPixel work for drawing in loop - c++

Question

This code draws a sine wave with function. In the following panning/zooming code, I am trying to understand how fWorldPerScreenWidthPixel is being used to draw the line segments.
WorldToScreen(fWorldLeft - fWorldPerScreenWidthPixel, -function((fWorldLeft - fWorldPerScreenWidthPixel) - 5.0f) + 5.0f, opx, opy);
It is setting opx and opy, but why is it subtracted from: fWorldLeft
It seems strange to want to start left of fWorldLeft in the for loop where it draws the line. fWorldLeft starts at -25.
I have included the necessary code to explain:
// Draw Chart
float fWorldPerScreenWidthPixel = (fWorldRight - fWorldLeft) / ScreenWidth();
float fWorldPerScreenHeightPixel = (fWorldBottom - fWorldTop) / ScreenHeight();
int px, py, opx = 0, opy = 0;
WorldToScreen(fWorldLeft - fWorldPerScreenWidthPixel, -function((fWorldLeft - fWorldPerScreenWidthPixel) - 5.0f) + 5.0f, opx, opy);
for (float x = fWorldLeft; x < fWorldRight; x += fWorldPerScreenWidthPixel)
{
float y = -function(x - 5.0f) + 5.0f;
WorldToScreen(x, y, px, py);
DrawLine(opx, opy, px, py, PIXEL_SOLID, FG_GREEN);
opx = px;
opy = py;
}
Call to set fWorldLeft:
// Clip
float fWorldLeft, fWorldTop, fWorldRight, fWorldBottom;
ScreenToWorld(0, 0, fWorldLeft, fWorldTop);
Sets fWorldleft:
// Convert coordinates from Screen Space --> World Space
void ScreenToWorld(int nScreenX, int nScreenY, float &fWorldX, float &fWorldY)
{
fWorldX = ((float)nScreenX / fScaleX) + fOffsetX;
fWorldY = ((float)nScreenY / fScaleY) + fOffsetY;
}
and while I'm at it, World to Screen:
// Convert coordinates from World Space --> Screen Space
void WorldToScreen(float fWorldX, float fWorldY, int &nScreenX, int &nScreenY)
{
nScreenX = (int)((fWorldX - fOffsetX) * fScaleX);
nScreenY = (int)((fWorldY - fOffsetY) * fScaleY);
}
Thank you!
Josh

Answer 1

Let's break it down
WorldToScreen(
fWorldLeft - fWorldPerScreenWidthPixel,
-function((fWorldLeft - fWorldPerScreenWidthPixel) - 5.0f) + 5.0f,
opx, opy);
A clearer way to write that would be
x = fWorldLeft - fWorldPerScreenWidthPixel;
WorldToScreen(
x,
-function((x) - 5.0f) + 5.0f,
opx, opy);
This transforms the position (x, f(x)) from world space to screen space and stores the result in (opx, opy). Let's see how these two variables are used:
for(...)
{
...
DrawLine(opx, opy, px, py, PIXEL_SOLID, FG_GREEN);
...
}
This draws a line from (opx, opy) to (px, py) (which is the current point on the function. (opx, opy) is the old point on the function. And this is exactly what you are doing with the initialization from above. You set (opx, opy) to a point that is one pixel outside of the screen to ensure that there are no gaps at the border.