Why do we use squares as the pixel shape if we are trying to approximate a triangle?
Staffjamesfong1
@JustinHuey1 Great question! The short answer is that a rectangular grid of sample points typically has the simplest implementation in both software (simpler code) and hardware (simpler manufacturing).
In principle, any 2D sampling pattern is possible, even ones where the samples are just randomly distributed on the screen! We will talk about that more when we cover anti-aliasing methods.
jiaheyi-maggie
I think this is a really cool idea, but I am wondering if there are methods that improve sampling by for example setting a percentage of area threshold that modifies the indicator function. For example, if a square is 80% inside the triangle versus 20% inside, we assign relative weights.
Staffmcallisterdavid
@jiaheyi-maggie Great idea, that would probably look better!
Here's another thing to think about: we can improve the indicator function, but the problem with any indicator function is that it's binary. In reality, computer displays can create different shades so we'll learn how to leverage that to make smoother looking edges in the next lecture!
Staffyirenng
@jiaheyi-maggie Yes, good insight. You will actually implement a version of your idea (by "supersampling") on the first assignment. And I will discuss the theory of why it works in the next lecture.
Why do we use squares as the pixel shape if we are trying to approximate a triangle?
@JustinHuey1 Great question! The short answer is that a rectangular grid of sample points typically has the simplest implementation in both software (simpler code) and hardware (simpler manufacturing).
In principle, any 2D sampling pattern is possible, even ones where the samples are just randomly distributed on the screen! We will talk about that more when we cover anti-aliasing methods.
I think this is a really cool idea, but I am wondering if there are methods that improve sampling by for example setting a percentage of area threshold that modifies the indicator function. For example, if a square is 80% inside the triangle versus 20% inside, we assign relative weights.
@jiaheyi-maggie Great idea, that would probably look better!
Here's another thing to think about: we can improve the indicator function, but the problem with any indicator function is that it's binary. In reality, computer displays can create different shades so we'll learn how to leverage that to make smoother looking edges in the next lecture!
@jiaheyi-maggie Yes, good insight. You will actually implement a version of your idea (by "supersampling") on the first assignment. And I will discuss the theory of why it works in the next lecture.
Stay tuned!