Hidden line removal algorithm

1. Hidden Line Removal

2. HLR - Introduction
• Hidden line removal (HLR) is an extension of
wireframe model rendering where lines (or segments
of lines) covered by surfaces are not drawn.
• Hidden line removal (HLR) is the method of
computing which edges are not hidden by the faces
of parts for a specified view and the display of parts
in the projection of a model into a 2D plane.
• It is considered that information openly exists to
define a 2D wireframe model as well as the 3D
topological information.

3. HLR - Introduction

4. HLR - Introduction

5. Visibility Techniques
Algorithms might be slow in calculation and storing
data. These techniques will rectify the problem.
• Minimax Test
• Containment Test
• Surface Test
• Computing Silhouettes
• Edge Intersection
• Segment Comparison
• Homogeneity Test

6. Minimax Test/ Bounding Box Test
• To check whether a point is in a given bounded
surface or volume and checks if two polygons
overlap.
Conditions

7. Containment Test
• Determines the given point is located in or out of the
polygon and to check the vertices of one polygon for
containment in the other.
• Types of Method
– Intersection Method
– Angle Method

8. Containment Test
Containment proceeds:
(a) If the sum of the angles is equal to zero, point P is outside the
polygon.
(b) If the sum is equal to 360°, point P is inside the polygon.

9. Surface Test/ Back Face/Depth Test
• The process used to determine which surfaces and
parts of surfaces are not visible from a certain
viewpoint.
Condition :
– Faces whose surface normal are
positive in Z direction for visible
surfaces
– Faces whose surface normal are
negative in Z direction for non visible
surfaces

10. Computing Silhouettes
• A set of edges that separates visible faces from invisible faces
of an object with respect to a given viewing direction is called
silhouette edges (or silhouettes).
• An edge that is part of the silhouette is characterized as the
intersection of one visible face and one invisible face.

11. Computing Silhouettes

12. Edge Intersection
• To determine the visibility of partially invisible edges.
• Calculate line intersections to determine edge
visibility.
y = y1 + m (xboundary - x1)
x = x1 + (yboundary - y1) / m
m = (y2 - y1) / (x2 - x1)

13. Segment Comparison (Scan Line)
• Utilizes the image’s raster scan.
• Segment comparison are performed in x & z plane.
• Visibility techniques are further performed for each
span by comparing depth and edge segments.

14. Homogeneity Test
• Utilizes neighbourhood points to test its visibility.
• A Point can be projected onto neighbourhood of
projection of points, then the neighbourhood of
point P is decided to be visible or invisible.

15. Hidden Line Algorithms
• Priority Algorithm
• Area Oriented Algorithm
• Overlay Algorithm

16. Priority algorithm
• This algorithm is also known as depth or Z
algorithm.
• Imagines that objects are modelled with lines
and lines are generated where surfaces join. If
only the visible surfaces are created then the
invisible lines are automatically removed by
this algorithm.

17. Priority algorithm
Face Priority
ABCD 1
ADFG 1
DCEF 1
ABHG 2
EFGH 2
BCEH 2

18. Priority algorithm
• ABCD, ADFG, DCEF are given higher priority-1.
Hence, all lines in this faces are visible, that is,
AB, BC, CD, DA, AD, DF, FG, AG, DC, CE, EF and
DF are visible.
• AGHB, EFGH, BCEH are given lower priority-2.
Hence, all lines in this faces other than
priority-1 are invisible, that is BH, EH and GH.
These lines must be eliminated.

19. • Identify Silhouette Polygons
• Quantitative Hiding (QH)
• Visibility of Silhouette segment
• Intersect the internal edges
• Display the edges
Area Oriented algorithm

21. • Applicable for curved surfaces by approximating
them as planar surfaces.
• u-v grid is used to make grid surface by making it as
straight edges.
Overlay algorithm
• STEPS:
– To Calculate uv grid using surface
equation.
– Grid Surface to Linear Edge
creation.
– Using proper visibility techniques
for required output.

22. Thank You