how to draw number 1 in 3d with shading
I of the best ways to make a simple line drawing of a solid or surface announced to popular out into 3-infinite is to shade information technology properly. In lodge to shade a cartoon realistically you must first decide where the light source causing the shade is positioned. Since almost of the natural light in our earth comes from to a higher place, our brains are accustomed to processing shadows cast by such calorie-free sources. For this reason, also as for simplicity, I suggest that you position the calorie-free source directly above the object.
Hither is a sequence of drawings designed to show how light from to a higher place might affect various surfaces:
**ARTIST'S NOTE** Whatever 3 dimensional object in the real globe would non necessarily be afflicted by calorie-free in this manner since existent world light almost e'er involves multiple indirect lite sources. Also, these objects bandage no shadows every bit any existent world object would, since the mathematical objects nosotros draw float in empty space.
While looking at these drawings you lot may accept notices some of the following:
-Each aeroplane is shaded just one color grey.
-Planes closer to the light source or viewer are proportionally lighter.
-Planes angled more than towards the light source are proportionally lighter.
If you lot stick to these simple rules when drawing planar surfaces and solids, they will appear to be three dimensional.
You lot may by now have noticed that near of the surfaces nosotros will be cartoon are not planar, only rather are smooth and curvy. Here's one more shaded cartoon to assistance yous empathise how to shade a curved surface:
Compare this cartoon to the terminal drawing in the previous sequence of pictures. You will find that the but significant differences betwixt the ii drawings are the shape of their outlines and the presence or lack of inner outlined planes. If we had rounded out the planar drawing'due south outline and smudged away its inner lines, we would take gotten the spherical drawing.
In math we are used to thinking of polish, curvy surfaces every bit having tangent planes at every betoken. The easiest style to shade such surfaces is to imagine what color some of these tangent planes would be given the position of the light source, and so to interpolate between these planes. In this instance, interpolating = smudging. The all-time tools for smudging are erasers and fingers.
Extra Shading Tips
1. Use a 2B (or higher, 6B is best) pencil to shade. Don't use H pencils because they accept harder lead and won't shade smoothly and darkly. I recommend a refillable mechanical pencil. Always accept an eraser on hand -- information technology tin can be used to brand an area white if rubbed with hard or to smoothly smudge a gray expanse if rubbed with lightly.
2. Before shading more complicated surfaces it tin be helpful to lightly draw in some inner contour lines to make sure that yous empathize exactly what the surface looks like in between its outlines and piece curves. Take f(x,y) = 10<^2> - y<^2> for example:
These contour lines make it easy to run across how the surface curves in three-space. They were drawn by taking judge slice curves at very small intervals in both the fixed x and fixed y directions.
3. If you lot hate using pencils you may want to try shading by hatching and crosshatching. The basic thought of hatching is that an surface area of alternate black and white stripes appears greyness to the eye. Changing the frequency of the stripes changes the darkness of the gray color; more stripes per area means darker greyness. Crosshatching is hatching in two directions over the same area. Crosshatching produces darker grays than hatching since there are more blackness stripes per area. Here are some hatching and crosshatching examples:
Source: https://www.math.brown.edu/tbanchof/DrawingTutorial/3dshading.html
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