Wednesday, October 15, 2008

linear perspective basics

Two drawings are needed to construct a perspective drawing. A third is often necessary, but can be embedded in the second. The first is a map that gives scalable, 2-dimensional information about the orientation of viewer-to-object. I call this the Setup. It's often a plan that includes the viewer's location (SP). What's missing is vertical measure: eye height above ground of the viewer and the height/elevation of the object. (that missing elevation is very often the useful third document) Kevin Forseth's book has very clear illustrations. Here is an example of a Setup from his book:
station point (SP): the putative position of the viewer

line of sight (LOS): a straight line, often parallel to the ground, from the eye of the observer to the center of a scene

cone of vision (COV, FOV) : a peripheral limitation to the field of view -- a cone whose apex is at the station point and whose angle is between 35ºmin-60ºmax

picture plane (PP): an imaginary plane, perpendicular to the line of sight, from which the scaled measure of objects may be taken. In a one-point perspective, the picture plane can be coplanar with an elevation or section.

horizon line (HL): appears to cross through anything standing at the same height above ground as the eye level of the viewer; once it has been assigned a numerical value, the height of volumes on the ground can be inferred. Its usefulness is broad but still limited, and works most predictably when the line of sight is perfectly horizontal and parallel to the ground.

center of vision/central vanishing point (CVP): The geometric center of a perspective construction. The point where the line of sight intersects the picture plane, and the vanishing point for any lines oriented perpendicular to the picture plane. A perspective composition can be cropped such that the center of the construction is no longer located in the center of the frame.


Monday, October 13, 2008

busman's holiday for perspectivists


A holiday for some. With no competition from the day job, a student perspectivist can buckle down, locate all the furniture in the interior perspective, figure out the height of the windows, indicate the ins-and-outs of door jambs, soffits and bay windows, bring it all to class tonight and -- heck, shed some light on it, too.

Wednesday, October 8, 2008

b/w interiors

Per student request, here are 3 black and white interior perspective drawings. Click on an image to view slightly larger. charcoal pencilink and marker
Images ©J.F. Mahoney, all rights reserved.

Tuesday, October 7, 2008

going deep

In the world of flat geometry, a right isosceles triangle has equal sized legs and a 45º angle. One can divide a vertically-striped plane into a grid of equal squares using the 45º diagonal.This same plane's set of parallel lines, when laid down into the geometry of linear perspective, appear as rays that converge as they recede. Their convergence is governed by the central vanishing point C in this diagram based on Kevin Forseth's useful book on perspective: Since we're no longer in flat space, a diagonal line is at a virtual 45º. A protractor laid on the drawing will not measure 45º.
The rate at which equal intervals diminish in size as they recede is a affected by how far the measured field/back wall/picture plane is from the observer. This process of representing space fixes the viewer's distance from the virtual scene. The distance between the viewer(SP) and the viewed object (in this case, the back wall) is related to the distance between C, the center of vision and the vpD, or diagonal vanishing point. A perspectivist can slide the back wall forward to make the viewer feel closer to it. 

Increasing the distance (on the HL) between the vpD and C, would flatten the virtual 45º diagonal, compress the receding intervals into a smaller space on the page, and give the impression that the scene is farther from the observer. Note that the size of the back wall is the same as in the drawing above. By moving the vpD away from the central VP, the "measured" distance, or depth, between that wall and the observer appears more compressed.

Thursday, October 2, 2008

black holes

I had been working with a retail client on look-and-feel, sketching different stations of the retail experience and views unique to visiting a new location in Manhattan. The store design crew sent many typical product .jpg photos and architectural .dwg files to a 3d modeler, who created an animated fly-through for concept presentation to the CEO. Except for the fixture design, the layout and most of the interior details were complete.
Their boss found the design stiff and unfriendly. Photos of product had been wrapped around shapes that didn't match the products' proportions. Product was sparsely distributed and -- nightmare to any retailer -- nobody was in the store! Perhaps most painful for the design crew (apart from the uncannily familiar soundtrack) was how details that had not been fully worked out appeared: black polygons, virtual voids, stealing a show that could have been about how well the space was working. The concept was presented again, using quick sketches, and it moved along, approved. Later, a technique was developed to embed the brand's video advertising and music into sketch presentations.