Raytracing (Part 5) - Intersection with Cubes, Convex Polyhedra, and Meshes, Slides of Computer Graphics

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Computer Graphics Raytracing (Part 5)

Today..

n Cube and mesh hit( ) functions

n Antialiasing

Recall: Candidate Interval (CI)

n Define Candidate Interval (CI) as time interval during which edge might still be inside CVV. i.e. CI = t_in to t_out

n Conversely: values of t outside CI = edge is outside CVV

n Previously used CI initialized to [0,1], now can exceed this range

n Initialize CI to (-infinity, infinity)

t

t_in t_out

CI

Candidate Interval (CI)

Example to illustrate search for t_in, t_out

Note: CVV is different shape. This is just example

Testing against Planes

n To solve for intersection times with each plane, put ray

equation into implicit equation for plane

n And t_hit is given as

n Where numer = m. (B - S)

n And denom = m.c

S t B

F P P B

m c

m

denom

numer

t =

Testing against Planes

n Where numer = m. (B - S) , denom = m.c

n If denom = 0, ray is parallel to plane, numer determines if

it is wholly inside or outside

n numer > 0, wholly inside n numer < 0, wholly outside

n If denom > 0, means ray is passing into outside half of

plane, since m.c are less than 90 degrees apart

n If denom < 0, means ray is passing into inside half of

plane, since m.c are less than 90 degrees apart

Intersection with Convex Polyhedra

n Implementation for cube function is nicely laid out in figure 14.23 of text. Please read it..

n We’ve seen enough hit functions to last you a life time

n Read on your own..

n For convex polyhedra, instead of 6 faces for cube, store i faces

n Find normal to face i, mi and hit point Bi. Use loop then as

for(int i=0;i < N;i++)

numer = dot3D( mi, Bi - S )

denom = dot3D( mi, c)

… continue same as cube

}

Intersection with Mesh

n We can then extend method to develop hit function for a mesh

n Retrieve normal of mesh and vertex 0

n Read mesh intersection part from book (1/2 page)

for(int f=0;f < numFaces;f++)

Vector3 diff;

Vector3 normal(norm[face[f].vert[0].normIndex);

Point3 point(pt[face[f].vert.vertIndex);

form diff = point – genRay.start

numer = dot3D(normal, diff)

denom = dot3D(normal, genRay.dir )

… continue same as cube

}