OTHER THINGS YOU SHOULD KNOW
CS 4363/6353
OVERVIEW
•
Matrix Stacks
•
Raytracing and NPR
•
Physics Engines
•
Common File Formats
MATRIX STACKS
•
Typically, matrices are stored in a stack to avoid this
•
Stacks give us the ability to rotate one body around another
•
Stacks are also how (character) animation is done
•
Let’s say we wanted to fly through the solar system
• You still have a camera matrix
• The sun has been translated (but probably not rotated)
MATRIX STACK EXAMPLE
Camera matrix
MATRIX STACK EXAMPLE
“Push” the camera matrix.
Note: everything is rotated
by our camera matrix…
Camera matrix
MATRIX STACK EXAMPLE
“Push” the translation of the sun
Sun trans matrix
Camera matrix
Order of operations
MATRIX STACK EXAMPLE
“Push” the translation of the sun
Combine everything on the stack
into one MV matrix, then draw
the sun. Trans first, then camera!
mMV
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
The Earth is both translated
Sun trans matrix
Camera matrix
Note: yes, yes… I know it’s not to scale…
MATRIX STACK EXAMPLE
The Earth is both translated
Earth trans matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
The Earth is both translated
and rotated (in that order), so
we push those on a separate
frame…
Earth rot matrix
Earth trans matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
WRONG! The matrices are
multiplied TOP DOWN!
Earth rot matrix
Earth trans matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
WRONG! The matrices are
multiplied TOP DOWN!
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
Combine everything on the
stack into one MV matrix,
then draw the Earth!
Order
MATRIX STACK EXAMPLE
mMV
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
What about the moon?
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
Well, the moon has a
translation…
Moon trans matrix
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
Well, the moon has a
translation… as well as
a rotation…
Moon rot matrix
Moon trans matrix
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
Well, the moon has a
translation… as well as
a rotation…
Moon trans matrix
Moon rot matrix
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
Order
MATRIX STACK EXAMPLE
Moon trans matrix
Moon rot matrix
So we combine everything
on the stack into one MV
matrix, then draw the moon
mMV
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
What if we want to
draw a little independent
spaceship?
Moon trans matrix
Moon rot matrix
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
POP the Moon stuff!
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
POP the Earth stuff!
Earth trans matrix
Earth rot matrix
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
POP the Sun stuff!
Sun trans matrix
Camera matrix
MATRIX STACK EXAMPLE
…Leaving us with just the
camera matrix. Then, we
can add the spaceship
matrices on top of that.
Camera matrix
MATRIX STACK EXAMPLE
Push the spaceship trans first!
Ship trans matrix
Camera matrix
MATRIX STACK EXAMPLE
Then the rotation! Why?
Ship rot matrix
Ship trans matrix
Camera matrix
MATRIX STACK EXAMPLE
Now that you have your MV,
draw the ship…
mMV
Ship rot matrix
Ship trans matrix
Camera matrix
RAYTRACING
•
Easy to read article at http://en.wikipedia.org/wiki/Ray_tracing_(graphics)
Note: there are independent reflection, refraction and shadow rays
EXAMPLES
(AGAIN, FROM WIKIPEDIA.ORG)
EXAMPLES
(AGAIN, FROM WIKIPEDIA.ORG)
RAYTRACING
•
Advantages:
• Realistic simulation of lighting
• Natural shadows
• Simple to implement (but not trivial)
• Heavily parallelizable
•
Disadvantages
• Still an approximation
• not truly photorealistic
• Must limit depth
• Recursively adds up light values of rays
• Ssssssssssssslllllllllllllllloooooooooooooooowwwwwwwwwwwwww
THE UNCANNY VALLEY…
•
“…holds that when human replicas look and act almost, but not perfectly, like actual
human beings, it causes a response of revulsion among human observers”
Final Fantasy: The Spirits Within
http://en.wikipedia.org/wiki/Uncanny_valley
NPR
(NON-PHOTOREALISTIC RENDERING)
•
Stylistic
• Water color
• Impressionism
•
Example: Toon Shading
• Geometry remains the same
• Shading changes
•
Commonly seen in video games
• Borderlands
http://en.wikipedia.org/wiki/File:Toon_Shader.jpg
WORKING WITH PHYSICS ENGINES
•
•
There are several out there:
•
Tokamak (open source, no longer maintained)
•
Bullet (open source – several commercial games and movies like “2012” and “Bolt”)
•
Havok (commercial – Ireland, loads of commercial games)
•
PhysX (commercial – Ageia/NVDIA, CUDA, uses PPU, tons of games as well)
Usually provide:
•
Gravity
•
Collision (between static and dynamic bodies)
•
Soft-body physics
•
Ragdoll physics
•
Vehicle dynamics
•
Fluid simulations
•
Cloth simulations
HOW WE USE THEM…
•
Physics engine is a black box
•
We “load” the physics engine
• Tell it which objects are dynamic
• Tell it which are static
• Define parameters, such as gravity, bounce and so on
•
During each frame of animation:
• Update the physics engine by a delta time
• Ask the physics engine for:
• The location of each dynamic object
• The orientation of each dynamic object
TOKAMAK EXAMPLE
•
Typically have a limited number of basic shapes
• Cube
• Capsule
• Sphere
•
Must declare variables to hold all of the objects in your scene
#include <tokamak.h>
neSimulator* gSim = NULL;
neRigidBody* gCubes[NUM_CUBES];
neRigidBody* sphere;
neAnimatedBody* floor1 = NULL;
neT3 t;
void setupPhysicsEngine() {
// This will define the size and shape of each cube
neGeometry* geom;
// length, width and height of the cube
neV3 boxSize1;
neV3 gravity;
neV3 pos;
float mass;
float fmass = 0.2f;
// The number of total objects the simulator has to keep track of...
neSimulatorSizeInfo sizeInfo;
// Fill in the size info about the environment
sizeInfo.rigidBodiesCount = NUM_CUBES+1;
sizeInfo.animatedBodiesCount = 1;
// total number of objects
sizeInfo.geometriesCount = sizeInfo.rigidBodiesCount + sizeInfo.animatedBodiesCount;
// total number of collisions possible n*(n-1)/2
sizeInfo.overlappedPairsCount = sizeInfo.geometriesCount*(sizeInfo.geometriesCount-1)/2;
sizeInfo.rigidParticleCount = 0;
sizeInfo.constraintsCount = 0;
sizeInfo.terrainNodesStartCount = 0;
gravity.Set(0.0f, -3.0f, 0.0f);
gSim = neSimulator::CreateSimulator(sizeInfo, NULL, &gravity);
// Setup a box - using loop
for (int i = 0; i < NUM_CUBES; i++) {
gCubes[i] = gSim->CreateRigidBody();
// Get the geometry object from the cube
geom = gCubes[i]->AddGeometry();
boxSize1.Set(1.0f, 1.0f, 1.0f);
geom->SetBoxSize(boxSize1[0], boxSize1[1], boxSize1[2]);
gCubes[i]->UpdateBoundingInfo();
mass = 1.0f;
gCubes[i]->SetInertiaTensor(neBoxInertiaTensor(boxSize1[0], boxSize1[1], boxSize1[2], mass));
gCubes[i]->SetMass(mass);
pos.Set(i%10-5, i/10+0.5, -30);
gCubes[i]->SetPos(pos);
}
// Create the sphere
sphere = gSim->CreateRigidBody();
geom = sphere->AddGeometry();
geom->SetSphereDiameter(2);
sphere->UpdateBoundingInfo();
sphere->SetInertiaTensor(neSphereInertiaTensor(2, fmass));
sphere->SetMass(fmass);
pos.Set(0, 1, -4);
sphere->SetPos(pos);
sphere->SetAngularDamping(0.01f);
// Create the floor
floor1 = gSim->CreateAnimatedBody();
geom = floor1->AddGeometry();
boxSize1.Set(100, 0.001, 100);
geom->SetBoxSize(boxSize1[0], boxSize1[1], boxSize1[2]);
floor1->UpdateBoundingInfo();
pos.Set(0, 0, 0);
floor1->SetPos(pos);
}
void display () {
degree += 0.1f;
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
gSim->Advance(0.015);
//Cubes
for (int i = 0; i < NUM_CUBES; i++) {
t = gCubes[i]->GetTransform();
cube_state[0][0] = t.rot[0][0]; cube_state[1][0] = t.rot[1][0]; cube_state[2][0] = t.rot[2][0]; cube_state[3][0] = t.pos[0];
cube_state[0][1] = t.rot[0][1]; cube_state[1][1] = t.rot[1][1]; cube_state[2][1] = t.rot[2][1]; cube_state[3][1] = t.pos[1];
cube_state[0][2] = t.rot[0][2]; cube_state[1][2] = t.rot[1][2]; cube_state[2][2] = t.rot[2][2]; cube_state[3][2] = t.pos[2];
cube_state[0][3] = 0.0f; cube_state[1][3] = 0.0f; cube_state[2][3] = 0.0f; cube_state[3][3] = 1.0f;
drawCube(…);
}
// Sphere
t = sphere->GetTransform();
sphere_state[0][0] = t.rot[0][0]; sphere_state[1][0] = t.rot[1][0]; sphere_state[2][0] = t.rot[2][0]; sphere_state[3][0] = t.pos[0];
sphere_state[0][1] = t.rot[0][1]; sphere_state[1][1] = t.rot[1][1]; sphere_state[2][1] = t.rot[2][1]; sphere_state[3][1] = t.pos[1];
sphere_state[0][2] = t.rot[0][2]; sphere_state[1][2] = t.rot[1][2]; sphere_state[2][2] = t.rot[2][2]; sphere_state[3][2] = t.pos[2];
sphere_state[0][3] = 0.0f; sphere_state[1][3] = 0.0f; sphere_state[2][3] = 0.0f; sphere_state[3][3] = 1.0f;
drawSphere(…);
glutSwapBuffers();
glutPostRedisplay();
}
COMMON FILE FORMATS
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.3ds – AutoDesk 3DS Max (legacy)
•
.blend - Blender
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.c4d – Cinema 4D
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.dae – COLLADA (xml)
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.fbx – AutoDesk
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.lwo – LightWave Object
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.ma/.mb – AutoDesk Maya
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.max – AutoDesk 3DS Max
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.md2/.md3 – Quake 2/Quake 3
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.pov – POV ray file
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.skp – Google Sketchup
•
.sldasm – SolidWorlds Assembly
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.smd – Valve’s format
•
.u3D – Universal 3D (3D Industry Consortium - xml)
THE .OBJ FILE FORMAT
•
Also called WaveFront OBJ
•
Text-based
•
Easy to work with and widely accepted
•
File specifies:
• Position of each vertex
• UVs of each vertex
• Normals of each vertex
• List of faces (triangles)
EXAMPLE
(HTTP://EN.WIKIPEDIA.ORG/WIKI/WAVEFRONT_.OBJ_FILE)
# List of Vertices, with (x,y,z[,w]) coordinates, w is optional.
v 0.123 0.234 0.345 1.0
v ...
...
# Texture coordinates, in (u,v[,w]) coordinates, w is optional.
vt 0.500 -1.352 [0.234]
vt ...
...
# Normals in (x,y,z) form; normals might not be unit.
vn 0.707 0.000 0.707
vn ...
...
# Face Definitions (see below)
f 1 2 3
# Vertices only
f 3/1 4/2 5/3
# Vertices/Texture coords
f 6/4/1 3/5/3 7/6/5
# Vertices/Textures/Normals
f ...
...
OTHER OPTIONS
•
Smooth shading
• s 1 – smoothing is true
• s off – no smoothing
•
Materials may be put into a separate .mtl file
• newmtl myMat
• Ka 1.000 1.000 1.000
#ambient white
• Kd 1.000 1.000 1.000
#diffuse white
• Ks 0.000 0.000 0.000
#specular off
• Ns 50.000
lighting equation)
# size of spec (s from our
• Tr
#transparency
0.9