I have a question here, can the first equation also be applied to 3D? If yes, is u a vector3D in 3D space?

Here, in the 2nd bullet, "Divide by distance of a from line ca", shouldn't there be 'b' instead of 'a'?

We can say that the bunny would then lie in the x-y plane

how is the triangle's depth mapped to a grayscale value? is it proportional to the real distance between the triangle and the camera?

can someone explain this to me please...

I think it depends on the the function u(x). Correct me if I am wrong: If u(x) is, say, 5, then, f(u) = 5 and for all x (0, 1), the map is uniform. However, if, say, u(x) = 5x, then, for all x (0, 1), it will be non-uniform for intermediate values

What is an anisotropic filtering like? How to combine multiple samples?

Is the mapping linear?

If scaling x,y and w at the same time, it is like the bunny is scaled down to the origin?

This is not a linear map?

The triangles have different colors, so the shading difference lets you see which triangle is assumed to be "covering" the pixel for edge cases.

What's the difference between the light gray and dark gray shading?

One thing you might try is breaking u and v into components along w and perpendicular to w, making an argument for these components separately, and then putting them all back together.

Oh Sorry! I made a mistake there, where I thought u and v are pointing in the same direction. The right way would be calculating the area of parallelograms I think

I was not very clear about this in class because I confused the meaning of dX_i and dY_i. The slide is actually correct. What makes it work out:

-> Notice that dX_i is the difference between the X coordinate of P_{i+1} and P_{i} -> Similarly, dY_i is the difference between the Y coordinate of P_{i+1} and P_{i} -> Notice that the outward pointing normal n of this line is [ dY_i, -dX_i ]^T

Now the math works out to what I derived on the board: E_i(x, y) = E_i(q) = (q-P_0) . n

(sorry about the LaTex notation)

Location is NSH 3002

As I mentioned in class -- Assignment 0.0 is due today! Assignment 0.5 is due Wednesday.

Yes, thank you!

I see this for 4. How will you show 5 with similar triangles?

Numerical integration is very common in graphics, in part because we often do not have nice smooth functions for phenomena we represent or measure.

I found a small typo in this slide. The last row in the result matrix in the last bullet point should be (a_{1,z}u_{1} + a_{2,z}u_{2}).

Both property 4 and 5 can be proved geometrically using similar triangles

In general, this integral could be difficult to solve exactly. Will we have to use numerical integration techniques whenever we want L2 norms, or will most of our functions have integrals that are easy to compute?

You can add comments or ask questions by clicking on the slide and typing into the text box underneath.

Could do absolute value instead of max if surface is double-sided, right?