As a look-ahead:

• lab 8 will be on 3D Camera.
• Project 4 will be due next Monday, rather than at the end of Thursday this week. That's because you'll be implementing the camera tech we will talk about today into it.
• Lab 9/10 will be on a particle system (this will be good for Final Project Sketch)
  • Also includes boids, or a group background animation for things like NPCs
  • And then another advanced rendering technique (TBD by Zoe later)
• Final Project: demoed in person during Finals Week
  • There's two required check-ins in-person to make sure you're manage is timed.

This week, we'll discuss:

• virtual camera
• review of the graphics pipeline, namely how projections works as well as clipping & culling
• a grab bag exposing you to effects for your Final Project
• advanced graphics topics

Animation: Control Along Curves

When we did hiearchical modeling, we would instead probably want to animate over a curve instead:

We might also want to move some point along a curve that isn't linear, like shown above. But how do we represent these curves? The P4 code has some of these splines, and if we look in there in Bezier.h we can get a better idea of what's going on.

The Camera: The V Matrix

We use the View matrix V as a way to translate, rotate, etc. the world we've already made.

We already have this, so now we need to first know what the position of the camera/eye is in the world. We can use glm::LookAt() to generate this V matrix:

glm::LookAt(
	vec3 eyePositionInTheWorld,
	vec3 eyeLookAtPoint, // essentially helps generate the lookingDirection from eyeLookAtPoint - eyePositionInTheWorld
	vec3 UpVector, // almost always (0,1,0). Most games do this. Generates the 'barell-roll' angle in case we want to rotate our view in that plane. 
);

So for this camera you need to do:

• Pitch and Yaw (look anywhere)
• WASD (go anywhere)
  • Translate eyePositionInTheWorld to move anywhere

We'll talk about Pitch and Yaw in more detail here.

Pitch and Yaw

We can use $\alpha$ as pitch and $\beta$ as yaw. You can get the eyeLookAtPoint from getting the spherical coordinate into cartesian:

and really when we move the mouse some position $\mathrm{\Delta }x,\mathrm{\Delta }y$ we want to just change these angles as:

And $\beta$ is very similar.

Strafing and Dollying

Say we want to strafe left/right. How do we translate to do that? You don't just move along $x$. That is fixed in the world. What we really want is to strafe relative to our view vector $\overrightarrow{v}$:

Thus we need the cross product!:

and for dollying, we just move in the direction of the view vector:

Defining our Camera

We'll make a Camera Object Camera which will use our function above.

We'll want to use orthonormal basis vectors which are vectors of:

• unit length
• perpendicular to one another

Namely, we can do a change of basis to convert our standard world basis vectors to our camera basis vectors:

Namely, we just use two matrices, the translation matrix, and the rotation matrix:

We form these basis vectors for the camera $u,v,w$ as:

• $w$ is just $\frac{-\text{gaze}}{||\text{gaze}||}$
• $u={\overrightarrow{v}}_{up}\times w$
• $v=w\times u$

Look at how these are generated:

• $w$ is generated by flipping our ${\overrightarrow{v}}_{view}$ vector, then normallizing it.
• $u$ need to be perpendicular to $w$ (we need an orthonormal basis, remember), then we want to have $u$ not point in the direction of ${\overrightarrow{v}}_{up}$ since we usually have the second vector (like $\overrightarrow{y}$) to be the up direction. Hence $v$ needs to be that, so $u$ needs to be perpendicular to ${\overrightarrow{v}}_{up}$.
• $v$ is just perpendicular to $u,w$.