Lecture #2: Points. Lines. Triangles

Rasteriztion theory

It’s possible construct any image using the next operation:

• draw a point
• draw a line
• draw a triangle

“Color space” experiment

Deduction phase

• Pixel is 3 colored light sources
• Does variation of pixel give a different color?
• What about performance?

“Color space” experiment

Experiment

Let’s implement it together

“Color space” experiment

Reference

“Color space” experiment

What is the new knowledge?

• We’re able to draw any color from a gamut using variation of intensity of red, green, and blue colors

Simple line equation

\[y = ax+b\]

Equation from 2 points

\[a = \frac{y_1 - y_2}{x_1 - x_2}\] \[b = y_1 - x_1\frac{y_1 - y_2}{x_1 - x_2}\]

\[y= y_1 + \frac{y_1 - y_2}{x_1 - x_2}(x - x_1)\]

Naïve’s draw line algorithm

slope = (y_begin - y_end)/(x_begin - x_end)
for x in range(x_begin, x_end):
    y = y_begin + slope*(x - x_begin)
    draw_point(x, round(y))

[1]

“Draw line” experiment

Deduction phase

• Line could be represent as set of pixels
• To draw line we can use Naïve’s draw line algorithm
• What about performance?

“Draw line” experiment

Experiment

Let’s implement it together

“Draw line” experiment

Reference

“Draw line” experiment

What is the new knowledge?

• Naïve’s draw line algorithm has an issue with zero-division
• Naïve’s draw line algorithm has an issue with empty spaces
• Naïve’s draw line algorithm doesn’t fit to draw lines

Bresenham’s draw line algorithm

Improvements of Naïve’s draw line algorithm

• Mirror of the best range
• Don’t calculate a line function
• Use error calculation to increment y value

[1]

“Draw line” experiment

Deduction phase

• Line could be represent as set of pixels
• To draw line we can’t use Naïve’s draw line algorithm
• To draw line we can use Bresenham’s draw line algorithm
• What about performance?

“Draw line” experiment

Experiment

Let’s implement it together

“Draw line” experiment

Reference

“Draw line” experiment

What is the new knowledge?

• Bresenham’s draw line algorithm is pretty good to use for draw lines

Famous references

Stanford bunny

[2]

Famous references

Utah teapot

[3]

Famous references

Cornel box

[4]

Famous references

Sponza palace

[3]

Wavefront OBJ format

• # - comment
• v - vertex
• vn - normals
• vt - texture coordinates
• f - face (polygon) - list of vertexes, normals, and tex coordinates [5]

Cornell box example

## Object floor
v  -1.01  0.00   0.99
v   1.00  0.00   0.99
v   1.00  0.00  -1.04
v  -0.99  0.00  -1.04

g floor
usemtl floor
f -4 -3 -2 -1

## Object ceiling
v  -1.02  1.99   0.99  
v  -1.02  1.99  -1.04
v   1.00  1.99  -1.04
v   1.00  1.99   0.99

g ceiling
usemtl ceiling
f -4 -3 -2 -1

“Read obj” experiment

Deduction phase

• Obj file contains faces
• Each face contains vertexes
• Does drawing line between vertexes in each face give us a wire frame image?
• What about performance?

“Read obj” experiment

Experiment

Let’s implement it together

“Read obj” experiment

What is the new knowledge?

• Image is not correct. We need more accurate translations