Transcript 3D Graphics Introduction Part 2 CIS 488/588 Bruce R. Maxim

3D Graphics Introduction
Part 2
CIS 488/588
Bruce R. Maxim
UM-Dearborn
5/23/2016
1
3D Data Structures
• Triangles
– Pros: very good, very fast
– Cons: need lots of them
• Quadrilaterals
– Pros: good, fast
– Cons: non-coplanar
• Polygons
– Pros: easy to model with them
– Cons: hard to draw, hard to clip
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Defining Polygons - 1
• Suppose we decide to model all polygons
using triangles
• Assume the rasterizer will clip triangles as
needed as they are drawn (avoiding the use
of 3D clipping in this chapter)
• To avoid redundant listing of vertex
information it is wise to use a vertex list to
define 3D shapes
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Defining Polygons – 2
• For a cube the vertices might be
POINT3D vertex_list[NUM_VERTICES];
vertex_list[0] = {x0, y0, z0};
…
vertex_list[7] = {x7, y7, z7};
struct typedef POLY_EX_TYP_2
{
POINT3D_PTR vlist:
int vertices[3];
} POLY_EX_2, *POLY_EX_2_PTR;
POLY_EX_2 face1 = {vertex_list, 0, 1, 2};
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Defining Polygons – 3
• One advantage of the vertex list method is
that you avoid vertex drift that results when
several copies of the same vertex are
transformed independently (known as
geometry cracking – as seen in Tomb Raider)
• Sometimes you need to separate the
polygons and vertex lists (esp. if you only
need to render 1 of thousands of triangles in
a surface)
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Defining Polygons – 4
• Another problem comes with clipping the
vertex list without examining the polygons
(you end up clipping any polygon the shares
the clipped vertex)
• To avoid this, you might need to adopt a
hybrid approach that involves defining and
transforming vertex lists and also convert
them to single polygons when necessary
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Defining Polygons - 5
// a polygon based on an external vertex list
typedef struct POLY4DV1_TYP
{
int state;
// state information
int attr;
// physical attributes of polygon
int color;
// color of polygon
POINT4D_PTR vlist; // the vertex list itself
int vert[3];
// the indices into the vertex list
} POLY4DV1, *POLY4DV1_PTR;
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Defining Polygons - 6
// a self contained polygon used for the render list
typedef struct POLYF4DV1_TYP
{
int state;
// state information
int attr;
// physical attributes of polygon
int color;
// color of polygon
POINT4D vlist[3]; // vertices of this triangle
POINT4D tvlist[3]; // vertices after transformation if needed
POLYF4DV1_TYP *next; // pointer to next polygon in link list
POLYF4DV1_TYP *prev; // pointer to previous polygon in LL
} POLYF4DV1, *POLYF4DV1_PTR;
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Defining Objects - 1
• Object contains everything needed for the 3D
pipeline even transformed coordinates
• Static arrays are used (they waste storage
but avoid allocation and deallocation of
storage)
• Limited to 64 vertices and 128 polygons
• Radius fields are used to assist in culling
• “dir” is used to track rotations as local
coordinates are overwritten
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Defining Objects - 2
typedef struct OBJECT4DV1_TYP
{
int id;
// numeric id of this object
char name[64];
// ASCII name of object just for kicks
int state;
// state of object
int attr;
// attributes of object
float avg_radius; // average radius of object used for
//collision detection
float max_radius; // maximum radius of object
POINT4D world_pos;
// position of object in world
VECTOR4D dir;
// rotation angles of object in local
// cords or unit direction vector user
// defined???
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Defining Objects - 3
VECTOR4D ux,uy,uz;
// local axes to track full orientation
// this is updated automatically during
// rotation calls
int num_vertices;
// number of vertices of this object
POINT4D vlist_local[OBJECT4DV1_MAX_VERTICES]; // local vertices
POINT4D vlist_trans[OBJECT4DV1_MAX_VERTICES]; // transformed ver
int num_polys;
// number of polygons in object mesh
POLY4DV1 plist[OBJECT4DV1_MAX_POLYS]; // array of polygons
} OBJECT4DV1, *OBJECT4DV1_PTR;
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Representing Worlds
• Can’t just throw dozens or objects made up of
hundreds of polygons into the graphics
pipeline without taking a performance hit
• In reality only a small portion of the game
world will be visible from any given viewpoint
• Terrain does not change much so its images
could be left in world coordinates avoiding a
local world transformation
• More advanced techniques are discussed in
later chapters
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3D Modeling Tools
•
•
•
•
•
•
Calagari trueSpace
Maya
LightWave
3D Studio Max
Blender
Moray coupled with a ray tracer like
Persistence of Vision (POV)
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PLG File Format - 1
• There are some modelers that produce PLG
files and utilities to convert DXF to PLG files
• Format
– Header line
object_name num_vertices num_polygons
– Vertex list (0 to n in x-y-z order)
x_coord y_coord z_coord
– Polygon list
surface_description n v1 v2 v3 … vn
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PLG File Format - 2
• Surface description code – 16 bits (can be
either hex or decimal)
H15 – 1 means interpret as bottom 14 bits as surface
map index otherwise use table interpret to S13S12
R14 – reserved should be 0
S13S12 – 00 solid shaded, 01 flat shaded, 10 metallic,
11 transparent
C11C8 – one of 16 color hues
B7B0 – brightness of color
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NFF File Format
• Neutral file format (virtual reality games)
• Supports
–
–
–
–
–
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Simple perspective frustrum
Background color descriptions
Positional light source description
Surface properties description
Polygon, polygon patch, cylinder/cone, and sphere
descriptions (in vertex format)
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NFF Example
v
from 0 2.0 2.0
at 0 0 0
up 0 1 0
angle 40
hither 1
resolution 512 512
l 0 5 0
l 0 2.0 2.0
f 0.000000 0.000000 0.000000 1 0 0 0 0
p 3
1.000000 -1.000000 -1.000000
-1.000000 -1.000000 -1.000000
-1.000000 -1.000000 -1.000000
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// viewport location
// positional lights
// fill light
// polygon format
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DXF File Format
• Binary and ACSCII versions originally
supported by AutoCAD
• Format
–
–
–
–
–
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Header Section (general model info)
Tables Section (definitions of named objects)
Blocks Section (lists entities for each block)
Entities Section (contains actual model entities)
End of File Marker
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Other File Formats
• 3DS
– Binary format produced by 3D Studio Max also has an
ASCII version
– Largely a file header followed by vertex and face
information
• COB
– Produced by Calagari trueSpace
– Vertex based format similar to 3DS
• .X
– Microsoft Direct X format, contains everything Direct
3D handles importing
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3D Mesh Translation
• Simply adjust its position vector
• To move an object by t=<tx, ty, tz>
object.world_pos.x = Object.world_pos.x + t.x;
object.world_pos.y = Object.world_pos.y + t.y;
object.world_pos.z = Object.world_pos.z + t.z;
• To move in elliptical path parallel to x-z plane
using absolute coordinates
x_pos = a * cos(angle);
y_pos = altitude;
z_pos = b * sin(angle);
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3D Mesh Rotation
• Need to track orientation relative to the axis
(to avoid problems like gimbal lock)
• Should rotate an object’s local coordinates
placing (0,0,0) at the object center
• Need an orientation vector “dir” the is aligned
pointing down the z+ axis
• “dir” is update any time the object is rotated to
keep track of its current orientation
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3D Mesh Morphing
• Scaling and shearing done in real-time to
make something look alive (e.g. breathing)
int up_down = 1;
float scale = 1;
while(1)
{
if (up_down == 1)
{
Scale_Object(&object, 1.05);
scale = scale * 1.05;
}
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3D Mesh Morphing
else
{
Scale_Object(&object, .95);
scale = scale * .95;
}
if ((scale < .75) || (scale > 1.25))
up_down = -up_down;
}
• Note eventually errors (drift) will start
creeping into the images and we will have to
refer to the original copies of each mesh and
apply the transformations to these instead
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Types of 3D Engines
•
•
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•
•
•
Space Engines (Star Wars:X-Wing)
Terrain Engines (Tread Marks)
FPS Indoor Engines (Unreal)
Ray Casters (Wolfenstein)
Voxel Engines (Medical Imaging)
Hybrid Engines (ray casting or polygons for
worlds and sprites for objects)
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Painter’s Algorithm
• Basic idea
– Sort surfaces and then draw so looks right.
– If all surface are parallel to view plane, sort
based on distance to viewer, and draw
from back to front.
– Worst-case is O(n^2)
– Otherwise, have five tests applied to each
pair to sort.
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Test 1: X overlap
• If the x extents of two polygons do not
overlap, then order doesn’t matter and
go to next pair.
• If x extents overlap, goto test 2.
+y
+x
Test 2: Y Overlap
• If the y extents of two polygons do not
overlap, then order doesn’t matter.
• If y extents overlap, goto test 3.
+y
+x
Tests 3 & 4
• Extend polygons to be a cutting plane
– If a polygon can be contained within the
cutting plane of the other, that polygon
should be drawn first.
– If neither can be contained, go to step 5.
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Tests 3 & 4
View direction
Polygon 1 is completely on one side of the
two planes “cut” by polygon 2.
Polygon 2
+z
Polygon 1
+x
Test 5
• Only needs to be consider if have
concave polygons.
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How to make it easier
• Use convex objects
• Avoid long objects (like walls) that can
overlap each other in multiple
dimensions
• Avoid intersecting objects and polygons
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Z-buffer
• Z-buffer holds the z-coordinate of every pixel
• Initialize all values to maximum depth
• Compute the z value of every point of every nonback facing polygon
– Not too hard if all polygons are triangles or rectangles
– Do this during the filling of the triangles
• If z of point < z in Z-buffer
– save the color of the current point and update Z-buffer
– otherwise throw away point and move on
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Ray Tracing
• Image space technique that mimics physical
processing of light
• Extremely computationally intensive
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Hidden surface removal
Transparency
Reflections
Refraction
Ambient lighting
Point source lighting
Shadows
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