Architectural Details and Ornaments

[Laurence Finston]

A couple more differences occurred to me: In MetaPost, figures are always ended with plain `endfig'. In effect, a MetaPost figure is always projected onto the x-y plane using the parallel projection. In 3DLDF, figures can be projected onto one of the major planes using the parallel projection or they can be projected with the perspective projection using a focus. If plain `endfig' is called, then the perspective projection is used with a default focus. I believe it's possible to change the default but it's been awhile since I programmed this feature and I never just call `endfig'. If I want the perspective projection, I always specify the focus.

The other difference involves the "hints" I mentioned above. Given two or more points, MetaPost will attempt to find the "most pleasing curve" that passes through them. However, when the MetaPost code is generated by 3DLDF, MetaPost doesn't "know" that the curves are supposed to be two-dimensional projections of three-dimensional curves, so the resulting curves are likely to be neither pleasing nor correct.

In order to prevent curves from "going out of shape", it is necessary to constrain them by increasing the number of points they contain. That's what's done when 3DLDF calls MetaPost: it passes the information about the curve (path) to MetaPost and has the latter calculate enough intermediate points so that the projected curve won't go out of shape when it is ultimately calculated by MetaPost.

[Laurence Finston]

The first image shows a single rapport of the pattern. For maximum flexibility, I decided to assign each path, i.e., the triangles with the wavy lines, the inner hexagons and the six-pointed stars, to a variable (p_x). The centers of the paths some of the vertices of the outer hexagons are also set to variables (the points Z_x).

The second image shows the first rapport and a single repeat in the horizontal direction with drawn lines only. In the third image, the paths are filled with computer-generated colors approximating the originals from Jones and Goury. I have no idea how close they are to the colors of the actual original.

In the fourth image, the colors, except for white, have been replaced by colors I scanned from backgrounds painted with gouache or watercolor. I used GIMP for the color replacement.

In the third and fourth images, more rapports were used and the pattern was repeated in the vertical direction. However, because of size constraints, a full repeat in the vertical direction can't be shown.

The fifth image shows two rapports, as in second image, but put into perspective.

The source code and a PDF file with these images is available here: Architectural Models
This is a link to the PDF file: https://www.gnu.org/software/3dldf/g...mbra_207_1.pdf