Project 1: Brush (Algo Answers)
You can find the handout for this project here. Please read the handout before working on this algo assignment!
Indexing Into Your Canvas
In Lab 2: Pencils, you learned that canvas data can be stored as a vector of RGBA
structs in row-major order. For such a canvas with width = 512
and height = 256
, please answer the following:
Row, Col -> Index
Given that the first pixel (index 0
) is at row 0
, column 0
, what is the index of the pixel at row 43
and column 242
?
Answer:
Explanation:
Index -> Row, Col
What is the row and column of the pixel at index 12345
in the vector?
Answer:
Explanation:
Mask Coverage
All of your brushes in Project 1: Brush
should be implemented using masks (see the Brush handout) which store a brush's opacity at certain point. As always, you should use a 1D vector to represent this 2D array of values.
This means that you will need to figure out what area of the canvas overlaps with the brush mask to iterate over in your drawing loop.
Answer the following questions for a linear brush with a brush radius
Mask Size
What is the size of your mask vector in pixels? Consider the 2D space you need to cover and how many pixels that is in total.
Answer:
Explanation:
The bottom-left pixel is
Calculating Mask Opacity
What is the opacity value of the mask at index
Answer:
Explanation:
The i-th element of the mask is
It is thus
From this, we can use Pythagoras' theorem to get the pixel's distance from the center pixel of the mask. This can then be plugged into a linear falloff formula to obtain the mask's opacity:
However, because this formula can take us into negative values at
If you got this question correct, you got an extra point on the algo assignment!
Finding Relative Coordinates
Suppose you click on a pixel at coordinates
What is the index of pixel
Answer:
Explanation:
The top-left pixel of the mask has index
Thus, the pixel
From this, you can just use the same "row, col -> index" conversion as before:
Color Blending
In Project 1: Brush
, you will blend the color of a brush with the color of canvas using the brush's mask. In that project, the canvas will be filled using our 4-channel RGBA struct, but for this exercise, assume that your image is grayscale and has only one channel, which we'll call intensity. Each pixel's intensity will be represented by a floating point value ranging from 0 (black) to 1 (white).
What is the value of the final intensity
As a sanity check, remember to consider the case when
Answer:
Explanation:
The fraction the brush contributes to the resulting color is
Using this as an interpolation weight, you can obtain the solution by linearly combining the brush's color,
Submission
Submit your answers to these questions to the "Project 1: Brush (Algo)" assignment on Gradescope.