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Ray Tracing

Computer Graphics and Imaging

UC Berkeley CS 184/284A

Discussion 06

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Week 7 Announcements

  • Homework 2 was due 3/4 - you have 3 slip days per assignment
  • Homework 3 Checkpoint is due on Friday 3/7. Homework is due 3/18.
  • Take-Home Exam Next Week.

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Ray Tracing Basics

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Ray Equation

r(t) = o + td

  • Where o is the position of the origin.
  • d is the direction of the ray.
  • t is time, and is ≥ 0.

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Ray Tracing

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Ray Tracing

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Worksheet Question 3

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Bonus Question!

How would you check if an intersection is inside a triangle?

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Bonus Question!

How would you check if an intersection is inside a triangle?

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Try placing the ray in this diagram to get intuition

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Try placing the ray in this diagram to get intuition

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Ray Triangle Intersection

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Last week: Ray-Plane Intersection

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Ray Triangle Intersection

But meshes are made of triangles, so we need ray-triangle intersection!

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Last week:

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Ray Triangle Intersection

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Ray Triangle Intersection Derivation

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Acceleration Structures

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Acceleration Structures Motivation

  • Meshes can be made of hundreds of thousands of triangles.
  • We sample at least one ray per pixel. (Imagine a 4K = 3840x2160 TV.)
  • Calculating intersections can quickly get expensive!

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Sneak Peek

In the next assignment, you will be able to render images like these!

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Idea: Bounding Volume Hierarchy

Internal nodes:

  1. Bounding box.
  2. Reference to children.

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Idea: Bounding Volume Hierarchy

Internal nodes:

  1. Bounding box.
  2. Reference to children.

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Leaf nodes:

  1. Bounding box.
  2. List of primitives in the box.

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Worksheet Question 2

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split this side

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split this side

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There are 2 valid splits!

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We’ll just consider this one.

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  • It’s fine if these bounding boxes intersect!
  • Key idea: we have partitioned objects into disjoint sets.

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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Using a Bounding Volume Hierarchy

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https://www.geogebra.org/3d/umn78ybr

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2.2. Using a Bounding Volume Hierarchy

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Hint: Axis-aligned ray-plane intersection equation

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2.2. Using a Bounding Volume Hierarchy

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2.2. Using a Bounding Volume Hierarchy

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2.2. Using a Bounding Volume Hierarchy

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Let’s Take Attendance.

  • The attendance form is in the header of the CS 184/284A course website: cs184.eecs.berkeley.edu/sp26/. You can also use this QR code:
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