Scan-Line Method Back-face Detection (Plane equation Method) Sweep Representation:

- It is an image-space method for identifying visible A fast and simple object space method used to - Sweep representations create solid by moving a
surface. remove hidden surface from a 3D object 2D shape (triangle, rectangle, polygon
- It computes and compares depth values along drawing is known as "Plane equation method". etc.) according to predefined rule (translating,
the various scan lines for the scene. A point (x, y, z) is inside a surface with plane rotating).
- Surfaces are processed using information stored parameter A, B, C & D if - Sweep representations are used to construct 3D
in the polygon
things. Sotable.
we cannot Ax + By + Cz + D < 0 object from 2D shape that have some
- An active
classlist of edges is formed for each scan
ExtraCurricularActivities i.e. it is in back face. kind of symmetry.
line which stores
{ float only those edges that
extra_curricular_marks; - For example, a prism can be generated using a
crossesfloat
the getExtraCurricularMarks()
scan line in order of increasing ‘x’. translational sweep and rotational sweeps
- Also a flag is set for each surface that is set on or can be used to create curved surfaces like an
off to indicate whether a position along ellipsoid or a torus.
a scan line is either inside or outside the surface. - There are two types sweep representation:
- Pixel position across each scan-line are processed For the left handed viewing system if the ‘z’ Translational Sweep: A 2D shape is translated by
from left to right. component of the normal vector is positive, a predefined translational vector.
- At the left intersection with a surface the surface then it is back face. If the ‘z’ component of the Example: following figure shows a translational
flag is turned on and at the right vector is negative then it is a front face. sweep of rectangle.
intersection point the flag is turned off. - For the right handed viewing system if the ‘z’
- We only need to perform depth calculation when component of the normal vector is
more than one surface has its flag negative, then it is back face. If the ‘z’
turned on at a certain scan-line position component of the vector is positive then it is a
front face.
Limitations: Rotational Sweep: A 2D shape is rotated around a
- This method works fine for convex polyhedral, predefined rotational axis.
but not necessarily for concave Example: following figure shows a rotational
polyhedral or overlapping objects. So, we need sweep.
to apply other methods to further
determine where the obscured faces are
partially or completely hidden by other objects
Advantage:
(e.g. Using Depth-Buffer Method or Depth-sort
- Any number of overlapping polygon surfaces can
Method).
be processed with this method.
- This method can only be used on solid objects
Limitation:
modeled as a polygon mesh.
- The scan line method runs into trouble when
surface cut through each other or otherwise
cyclically overlap. Such surface need to be divided.

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Boundary representation: Cubic spline
- The solids are described by its boundary surface. - It is used to set up path for object motions or to
Uses the description by vertices, edges provide a representation for an existing
and faces. object or drawings.
- The most common representation is the - Compared to higher-order polynomials, cubic
boundary polygons. splines requires less calculation and
- Will be considered only with solid border 2- memory and they are more stable. Compared to
manifolds(wherever the point is each edge lower-order polynomials, cubic splines
shared by two faces) i.e. the neighbors of any are more flexible for modeling arbitrary curve
point of the border point are on a disk (that shapes.
Advantages:
is to say that each edge is shared by two faces) - Cubic interpolation spline is obtained by fitting
- It provides a convenient representation for
the input points with a piecewise cubic
storing information about object interiors.
polynomial curve that passes through every
- They can represent arbitrary shapes and that
control points.
we can quickly analyze what is present at a
Suppose we have n+1 control points having co-
specific position in space.
ordinates
Disadvantages:
Pk = (xk, yk, zk) K = 0, 1, 2, 3, ... ... ... . , n
- Imprecise representation, high storage
demands and complex transformation
Wireframe representation
operations.
Octree Representation (Solid-object - If an object may be represented through the
representation) collection of points and line then it’s called
Solid Modeling
This is the space-partitioning method for 3D solid wireframe object.
Solid modeling is a consistent set of principles
object representation. Octrees are - It’s used to define skeleton of 3D objects in
for mathematical and computer modeling of
hierarchical tree structures that describes each terms of points and lines.
three-dimensional solids.
region space as nodes. They are used to - Mostly use in field of engineering drawings to
- A mathematical technique for representing
represent solid objects in some graphics system. represent the drawing of structure and
solid objects.
- Medical imaging and other applications that missing parts.
- An object with following specification is called
require displays of object cross sections - Wireframe represented object requires less
solid: Vertices, edges, surfaces, weight, and
commonly use octree representation. E.g. CT-scan. memory for storage and fast for display and
volume.
Octrees are used to partition a 3D space by surface rendering.
Solid modeling is based on complete, valid and
recursively subdividing it into eight octants. - In this method the scenes represented are not
unambiguous geometric representation of
Octant subdivisions continue until the region of realistic.
physical object.
space contains only homogeneous octants. - Complete: points in space can be classified.
- Octrees are often used in 3D graphics and 3D (inside/outside).
game engines. - Valid: Vertices, edges, faces are connected
properly.
- Unambiguous: there can be only one
interpretation of object.