By George K. Francis
Goals to motivate mathematicians to demonstrate their paintings and to aid artists comprehend the information expressed via such drawings. This e-book explains the picture layout of illustrations from Thurston's global of low-dimensional geometry and topology. It offers the foundations of linear and aerial viewpoint from the point of view of projective geometry.
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Goals to motivate mathematicians to demonstrate their paintings and to aid artists comprehend the guidelines expressed via such drawings. This e-book explains the picture layout of illustrations from Thurston's international of low-dimensional geometry and topology. It offers the foundations of linear and aerial point of view from the perspective of projective geometry.
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Extra resources for A Topological Picturebook
As long as the object line rotates in a plane, its vanishing point moves along a line, called the horizon line for the plane of rotation. Thus the picture plane comes into 1: 1 correspondence with the ideal plane under a projection along lines of sight. The vanishing points of object lines parallel to the picture plane are the ideal points for the picture plane. Its ideal line is the horizon for planes parallel to it. HORIZON AND ZENITH. Figure 2. Let me now take you through some easily remembered perspective tutorials.
An example involving nontrivial contours is this graphical transformation of a piecewise flat saddle, top center, to a smooth surface spanning the same border frame, bottom center. The square, horizontal face of 4(22) has two face edges (left) and two contour edges (right). The right column shows how the confluence of these two contour edges becomes a cusp. First, isolate a detail of this corner, 4(13), and bend the (new) borders. This initiates two contours, 4(23), which, in this case, cannot merge smoothly into a border or into each other.
Among the color plates in this book are some examples. Three photos, of an early version of the Duns Egg 6(11), show the linedrawing stage, the monochrome version, and a polychrome picture. I used color as a way of labeling matching surface features. For preparing and presenting polychrome pictures, 35mm slides have certain obvious advantages over transparencies. For their preparation I only need a slate blackboard, high-speed film and reasonably quick photo developing services. During the talk I can look at and point to the same image as the audience sees.
A Topological Picturebook by George K. Francis