| Midterm out today | |
| Project 1 demos |
| Today’s Readings | ||
| Nalwa 2.1 (handout) | ||
| Let’s design a camera | ||
| Idea 1: put a piece of film in front of an object | ||
| Do we get a reasonable image? | ||
| Add a barrier to block off most of the rays | ||
| This reduces blurring | ||
| The opening known as the aperture | ||
| How does this transform the image? | ||
| The first camera | ||
| Known to Aristotle | ||
| How does the aperture size affect the image? | ||
| Why not make the aperture as small as possible? |
| A lens focuses light onto the film | |||
| There is a specific distance at which objects are “in focus” | |||
| other points project to a “circle of confusion” in the image | |||
| Changing the shape of the lens changes this distance | |||
| A lens focuses parallel rays onto a single focal point | |||
| focal point at a distance f beyond the plane of the lens | |||
| f is a function of the shape and index of refraction of the lens | |||
| Aperture of diameter D restricts the range of rays | |||
| aperture may be on either side of the lens | |||
| Lenses are typically spherical (easier to produce) | |||
| Thin lens equation | ||
| Any object point satisfying this equation is in focus | ||
| What is the shape of the focus region? | ||
| How can we change the focus region? | ||
| Changing the aperture size affects depth of field | ||
| A smaller aperture increases the range in which the object is approximately in focus | ||
| The human eye is a camera | ||
| Iris - colored annulus with radial muscles | ||
| Pupil - the hole (aperture) whose size is controlled by the iris | ||
| What’s the “film”? | ||
| A digital camera replaces film with a sensor array | |||
| Each cell in the array is a Charge Coupled Device | |||
| light-sensitive diode that converts photons to electrons | |||
| http://www.howstuffworks.com/digital-camera2.htm | |||
| The coordinate system | |||
| We will use the pin-hole model as an approximation | |||
| Put the optical center (Center Of Projection) at the origin | |||
| Put the image plane (Projection Plane) in front of the COP | |||
| Why? | |||
| The camera looks down the negative z axis | |||
| we need this if we want right-handed-coordinates | |||
| Projection equations | ||
| Compute intersection with PP of ray from (x,y,z) to COP | ||
| Derived using similar triangles (on board) | ||
| Is this a linear transformation? |
| Projection is a matrix multiply using homogeneous coordinates: |
| How does multiplying the projection matrix change the transformation? |
| Special case of perspective projection | ||
| Distance from the COP to the PP is infinite | ||
| Also called “parallel projection” | ||
| What’s the projection matrix? | ||
| Scaled orthographic | ||
| Also called “weak perspective” | ||
| Affine projection | ||
| Also called “paraperspective” | ||