Sketches of the Gettysburg Battlefield

© Mahes Visvalingam and
    John C Whelan, June 2002

This project was undertaken in year 2001 on behalf of Bill Wright and Tom Kapler of Visual Insights Inc.  Our thanks to them for funding this application of P-stroke sketching through a grant to Mahes Visvalingam.  Our special thanks go to past and present PhD students for their input over the years, especially :

• Duncan Whyatt, for testing and evaluation of Visvalingam's algorithm for Line Generalisation
• Kurt Dowson, for applying this algorithm to the problem of P-stroke sketching and for use of his C software
  

Deliverables

    This project's deliverables included:

• A detailed explanatory report by Mahes Visvalingam (with a collection of relevant papers) concluding with ideas for articulation of sketching within an interactive 3D environment.
• The contour map; this was derived but users are advised to obtain more accurate USGS digitsed contours. 
• Matrices of Measures of Significance as scored by Visvalingam's algorithm for filtering by client.  These scores may be used to filter out scale-dependent convexities and concavities as explained by Visvalingam and Dowson (1998).    Some sample filtered maps are shown below.  The filtered cells seed the generation of P-strokes to sketch these curvatures.
• Sketches; these include 3 types of elements, namely:
  • P-strokes - as noted above
  • Formulated Silhouettes - see Whelan and Visvalingam (2002)
  • Shading based on row slopes; this indicated the scope for producing much clearer output than possible with OpenGL lighting.

The Gettysburg Battlefield

Maps and Photos

Modern map at :                           http://www.oswego.edu/Acad_Dept/a_and_s/earth.sci/geo_geochem/geol/getpark.html
Old map of the battlefield at:           http://www.lib.berkeley.edu/EART/digital/gettysb-lg.gif
Photos at:                                     http://www.angelfire.com/pa4/gettysburg/big.html

Reduced versions of some maps and photos, relevant to this project, are included here. (All copyright remains with the original authors)

The Problem

Profile Plots illustrate the motto - Data Rich - Information Poor!   Due largely to the nature of this terrain, light shaded images (see below), which were generated by our collaborators and us, were marginally better but also lacked sharpness and clarity.  This terrain with its relatively low undulating relief with low ridges, punctuated by a few prominent hills and a deep pit, also posed a challenge for our sketching algorithms and has identified new research objectives.

Curvatures

Sketches draw out the juxtaposition of prominent forms in the data.  All sketches are view-dependent.  The silhouettes establish the juxtaposition of relief elements   and indicate their outline forms.  Silhouettes alone are not enough for portraying this terrain, especially in map-like views assuming a high viewpoint. They need to be supplemented by other lines, indicating breaks of slope to mark the significant curvatures in the landscape.  These breaks of slope were abstracted using Visvalingam's algorithm; please note that this is not an image processing operator.  The output of the algorithm provides what we call a set of core cells.  These are the starting points for generating the P-strokes in the sketches.  Although the core cells can provide a set of  view-independent points for varied styles of sketching, the current style of P-stroke sketching (used to inaugurate our programme of research) requires view dependent filtering of convexities and concavities parallel and orthogonal to the view direction.  The following table gives the tolerance values used in the maps of core cells, which can be accessed by clicking on CORE CELL MAPS.

	Convex	Concave	Convex	Concave
CORE CELL MAPS for:	Parallel to View Direction		Orthogonal to View Direction
500m	500	500	500	500
Default tols	1000	4000	2000	1000
2m Sketch	2500	4000	5000	1000

 

The P-stroke Sketches with Formulated Silhouettes

This project was based on the 2.5D sketching system.  The oblique parallel projection used in this sketch has been fully explained elsewhere by Visvalingam and Dowson (1998).  In this projection, as implemented within the 2.5D system, the impression of a raised viewpoint is conveyed by shifting each row of the DEM up by a fixed y-offset.  The following annotated sketch shows the Gettysburg battlefield as seen from the South, with a vertical offset of 4m.  With this 10m resolution DEM, this produces a 40% tilt of the terrain block towards the user.  

1.  Formulated Silhouettes

These were designed to provide view-dependent outline profiles of hills and were fairly successful in many types of mountainous terrain (Whelan, 2001).   Whelan and Visvalingam (2002) explained their derivation and state the tolerances used.  With this low relief terrain, the filter's contol point was lowered  to 6 to include more points.   While this resulted in more continuous lines, it does generate some multiple strokes, for example in the bottom left.  Even so, the silhouettes provide better outlines than occluding contours with a  2m vertical offset, as shown below, but became quite sparse and frgmented with a 4m vertical offset. 

2.  P-Strokes

The P-stroke sketches are driven by two sets of parameters, namely a) the tolerances for filtering the locations where strokes should be placed and b) the extension rules for filtering the P-strokes, which are just parts of the surface profiles which are orthogonal to the view direction.  The parameters used are shown below. 

2m Offset Vertical Exaggeration of 1.5	Column Convex	Column Concave	Row Convex	Row Concave
Tolerances	2500	4000	5000	1000
Extension Rules	Minimal extension both sides	Minimum to left Full to right	Minimum downslope	Minimum to right
4m Offset Vertical Exaggeration of 1.5	Column Convex	Column Concave	Row Convex	Row Concave
Tolerances	1000	2000	2000	1000
Extension Rules	Minimal extension both sides	Minimal extension both sides	No extension in either direction	Minimum to right

KEY to extension rules:

Direction:            The stroke is extended from the filtered point along the profile lines to the right, left or downslope, where downslope.
                             uses the steeper of the minimum extensions to the right and left.
Length:
Minimum :          The stroke connects the filtered point to the next point either to the right, left or downslope (explained below)
None :                 The filtered point is connected to the next point on the right.
Full:                     The stroke starts at the filtered point and extends to, but does not include, the point with
                             a change in curvature or zero curvature. 

The following sketches show how the the inclusion of P-strokes provides better outlines of the landforms. Even so, the structure of the landscape is not easy to grasp without reference to other sources; other sample sketches show tat the 4m-offset sketches seen from the North are particularly difficult to grasp.

3.  Shading

The annotated sketch illustrates how even a very simple shading scheme can enhance the sketches.  Here, the colours are mapped to slope magnitudes across the view direction.  Current work is focusing on automatic generation of more subtle multidirectional shading schemes, which can also be used on planimetric maps.  Even the simple shading used here helps to group the linework and reveal the structure of the landscape.  

Conclusion

The sketches of this terrain, espcially those from a high viewpoint, are not as effective as the sketches of terrain with interlocking hills and plateaus and pose a challenge for future research.  However, the removal of redundant data produces a clearer picture of the landscape than light shaded images and other plots which show all the data.  Current work is focusing on the generation of real time vector sketches at interactive rates in a 3D environment.   This involves the evaluation of published methods for real time rendering of silhouettes and the design of view-independent styles for sketching the curvatures.