1. History of Cartographic Landscape Representation

2. Graphic representations  Where is the observer? Here are the 2 most typical mapping situations:  Above the surface with no perspective foreshortening  Often referred to as being ‘planimetrically-correct’  Useful for maintaining constant horizontal map scale  Anywhere else, usually with perspective foreshortening  Lines parallel to 1 or more world coordinate axes are shown as converging in the rendered illustration  Map scale changes continuously with distance from the viewpoint

3. Perspective geometry A cube in the 3D world is rendered in perspective Lines parallel to 3D axes of our choosing converge at selectable ‘vanishing points’ on the horizon Adobe Illustrator provides a tool to enable easy 3D perspective drawing

4. 3D rendering without perspective

5. A box with and without perspective geometry

6. Planimetrically-correct landscapes  Maintain constant horizontal scale to the limits of map projection  Hachures  Give very good impression of slope and aspect  Absolute elevations must be supplied by other means  Shaded relief  Like hachures, but using an airbrush technique  Contours  Excellent portrayal of absolute elevations  Slope and aspect discoverable by analysis of contours  Not as intuitive for users as hachures or shaded relief

7. Hachures Hachures are lines that show paths of steepest descent The image is a clip from a sample Dufour map provided for download by the Swiss Federal Office of Topography Guillaume-Henri Dufour was head of the Swiss Topographical Bureau in the mid 19 th century

8. Contours Image from http://street.umn.edu/Road/javahel p/HTML/Import_contour_map.htm http://street.umn.edu/Road/javahel p/HTML/Import_contour_map.htm On a map like this, ridges, slope breaks, peaks, course lines and other features pop out But most observers find it difficult to imagine the view of the scene from a particular point of view

9. Shaded relief Shaded relief maps are illuminated surfaces Brightness values correspond to the slope and aspect of a surface patch The light source for the scene is usually placed at a constant location for all points in the scene But not always…

10. Perspective representations  A sample of formats:  Landscape paintings  Block diagrams (Rudy Slingerland, Lobeck, Raisz)  Lithography (Imhof, etc)

11. Other factors in landscape rendering  Landscape images can serve many purposes  They can support scientific inquiry directly or indirectly  Photo-realistic styling  Essentially a photographic, more or less objective view  Non-photorealistic styling  Somewhat more subjective interpretation  ‘Painterly’ style  Pen and ink style

12. Landscape paintings  Thomas Cole, “The Oxbow”  (1836, from Wikipedia)  Follows rules of perspective geometry  Many other landscape elements (other than surface features) are included  Possible vertical exaggeration  For us, a ‘painterly’ example

13. Perspective Landscape Rendering  Demonstrated in Tuscan landscape paintings by da Vinci  Extended to woodcuts in the 16 th century by Murer and others Section of Map of Zurich, Murer, 1566Study of a Tuscan Landscape, Da Vinci, ca. 1473

14. Modern pen and ink landscape illustrations  William Henry Holmes, “Mesa Verde”  (1895, from David Rumsey map collection)  Intended to show surface processes  Simplicity of linework lends itself to interpretation of surface

15. Block diagrams Lobeck, Block Diagrams, 1958 Large scale, perspective view of surface and substructure

16. Lithography Image from Cartographic Relief Presentation, p. 255

17. Numeric representations  Digital elevation models (DEMs)  Vector (TIN)  Raster (grid cell)

18. Geometry and landscapes  What are we trying to do?  Realistic or abstract impression?  Navigation? Surface analysis?  What models do we need?  Planimetrically-correct?  Perspective?  Other? Picasso perspective?  Modern GPUs can do all this and more Picasso, La Rue des Bois or Paris, August or September 1908, https://www.moma.org/collection/works/80660?locale=en

19. Photorealistic representations  Standard shaded relief presentation with draped photography  Can we do better than this?  We should at least try!!

20. Non-photorealistic representations (NPR)  Line drawings can show surface trends  What other kinds of things can we do?  If you can imagine it, you can draw it