6-RayCasting

# 6-RayCasting - 3D Rendering and Ray Casting Jason Lawrence...

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3D Rendering and Ray Casting Jason Lawrence CS 4810: Graphics Acknowledgment: slides by Misha Kazhdan, Allison Klein, Tom Funkhouser, Adam Finkelstein and David Dobkin

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Rendering • Generate an image from geometric primitives Rendering Geometric Primitives Raster Image
Rendering • Generate an image from geometric primitives Rendering 3D 2D

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3D Rendering Example What issues must be addressed by a 3D rendering system?
Overview • 3D scene representation • 3D viewer representation • Ray Casting

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Overview • 3D scene representation • 3D viewer representation • Ray casting How is the 3D scene described in a computer?
3D Scene Representation • Scene is usually approximated by 3D primitives o Point o Line segment o Polygon o Polyhedron o Curved surface o Solid object o etc.

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3D Point • Specifes a location Origin
3D Point • Specifes a location o Represented by three coordinates o Infnitely small typedef struct { Coordinate x; Coordinate y; Coordinate z; } Point; (x,y,z) Origin

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3D Vector • Specifes a direction and a magnitude
3D Vector • Specifes a direction and a magnitude o Represented by three coordinates o Magnitude ||V|| = sqrt(dx dx + dy dy + dz dz) o Has no location typedef struct { Coordinate dx; Coordinate dy; Coordinate dz; } Vector; (dx,dy,dz)

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Linear Algebra: a Little Review • What is…? V 1 · V 1 = ?
Linear Algebra: a Little Review • What is…? V 1 · V 1 = dx dx + dy dy + dz dz

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Linear Algebra: a Little Review • What is…? V 1 · V 1 = (Magnitude) 2
Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 =

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Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 = ||V 1 || || V 1 || cos( Θ )
Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 = ||V 1 || || V 1 || cos( Θ ) = cos( Θ )

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Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 = ||V 1 || || V 1 || cos( Θ ) = cos( Θ ) = cos(0)
Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 = 1

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Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 = 1 V 1 · V 2 =
Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 = 1 V 1 · V 2 = ||V 1 || || V 2 || cos( Θ )

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Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors. • What is…? V 1 · V 1 = 1 V 1 · V 2 = ||V 1 || || V 2 || cos( Θ ) = cos( Θ )
Linear Algebra: a Little Review V 1 · V 1 = (Magnitude) 2 Now, let V 1 and V 2 both be unit-length vectors.

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6-RayCasting - 3D Rendering and Ray Casting Jason Lawrence...

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