Mark Nelson mjas@itu.dk

Rendering algorithms

Fall 2013 www.itu.dk

Last lecture: Wireframe projection

Wireframe -> opaque

Starts the same Transform vertices to (x,y) coordinates But instead of connecting the 3 vertices, flood-fill it with a color

But, how to deal with overlapping triangles?

Occlusion

Wireframes have no occlusion

Front and back side of objects are visible

If surfaces are opaque, that won’t do

How do we draw only visible surfaces?

Painter’s algorithm

Simplest solution

Sort triangles from back to front by center z-coord

Draw in order

Further-front triangles overwrite further-back ones

Painter’s algorithm

Painter’s algorithm downsides

Wasted drawing effort Triangles are drawn only to be overwritten

Possible artifacts since it only sorts by triangle centers

Scanline algorithm

Line by line

Find all triangle edges that intersect this line Start scanning left to right When we encounter an edge:

Add triangle to stack if it’s not on it (starting edge) Remove triangle if it was already on the stack (closing edge)

Draw pixel that corresponds to nearest triangle on stack

Simple ray-casting

From viewport, draw a ray from each pixel until it hits the first surface

Render that pixel

Simple but inefficient

Z-buffering

Render triangle to (x,y) framebuffer but also save the z’s

Z buffer: current z-depth of every pixel

Don’t write a pixel to the framebuffer if z > zbuffer

Optimization: draw front to back to minimize overwrites

Z-buffering / scanline

Generally combined

Proceed in scanline order Z-buffer for occlusion test

Why not stack-based scanline algorithm? Z-buffer correctly handles each pixel

Hierarchical z-buffer

Optimizations

Z-buffering stops us from rendering some unnecessary pixels

Can we avoid entire unnecessary triangles?

Frustum culling

Exclude triangles outside the frustum Clip triangles on the edges to the edge

Can be done either in view space or clip space

Occlusion culling

Fast-fail completely invisible triangles

E.g. ”early z test”

Potentially visible set algorithms

Some alternative perspectives Isometric graphics

Parallel projection, tiled, fixed viewing angle Graphics can therefore be predrawn to fake 3d The angle is the one where axes have the same scale Rotated 45 degrees around vertical, 35.264 around horizontal In pixel art, approximated with a 2:1 ratio

Oblique projection Fake 3d Draw a 2d front view of the object, and then a skewed 2 side view Depth often foreshortened (e.g. 0.5)

Isometric (Age of Empires 2)