Ray tracing

What is it?

Formulas

$$\norm{o + t\,d - c}^2 = R^2 \implies t^2 + 2t\,d\cdot(o - c) + \norm{o - c}^2 - R^2 = 0 \quad (\norm d = 1)$$

ray–sphere intersection: a quadratic

$$r = d - 2(d\cdot n)\,n$$

reflection

The mathematics behind it

• Bisection method★★★★★frequent

  Intersecting rays with implicit surfaces or height fields often brackets the hit and bisects.

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

What depends on it

• Signed distance fields and ray marching
• The rendering equation