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extrusion |
The extrusion object extrudes a 2D shape along a path. Here is an example, and here is the minimal syntax: ex = extrusion(pos=..., shape=...) The pos attribute is a list of points like the pos attribute of a curve object. The shape attribute is a list of x-y pairs describing the perimeter of a 2D surface, such as[ [2,0], [0,4], [-2,0], [2,0] ]. This 2D shape is extruded along the points specified by the pos list. The extrusion object is not yet available in Jupyter VPython. Other attributes An extrusion is made out of quads and triangles which are then made into a compound object for speed of display. You can make additional copies of an extrusion by cloning it. You can move an extrusion by specifying a new origin, and you can change its size, axis, up, color, opacity, shininess, and emissive, as with other objects, but note that color and size are "multiplicative"; see compound. Here are additional attributes that can be specified when creating an extrusion but cannot be changed later: show_start_face and show_end_face By default, these attributes are True and the start and end faces are displayed. If you set one of these to False, that face is left open. These attributes have no effect if the path is closed. start_face_color and end_face_color By default,the starting and ending faces are given the same color as the rest of the extrusion, as specified by color, but you can specify that other colors be used for the starting or ending face. These attributes have no effect if the path is closed. smooth By default, adjacent normals for which the cosine of the angle between them is greater than 0.95 (corresponding to an angle of 18 degrees) are averaged so as to smooth the adjacent surfaces. You can set smooth to a looser criterion for more smoothing. For example, setting smooth=0.9 will smooth adjoining surfaces whose orientation differs by 53 degrees, a much looser criterion. The three steps to making an extrusion 1) Create a 2D shape, either by giving a list of points or by choosing a shape from a supplied library of common shapes. Here are three examples. The first creates a triangle by listing 2D points. The second example creates a circular shape from the shapes and paths library, and the third creates a rectangular shape, using the shapes library. tri = [ [2,0], [0,4], [-2,0], [2,0] ] circ = shapes.circle(radius=3) rect = shapes.rectangle(width=0.2, height=0.4) A shape must be closed. That is, the last point must be the same as the first point. 2) Create a path along which to extrude your shape (just like the pos attribute of a curve object), either by giving a list of points or by choosing a path from a supplied library of common paths. Here are two examples. The first is a triangular path. The second chooses a circular path in the xz plane, and the third chooses a rectangular path in the xz plane. tripath = [ vec(1,0,0), vec(0,0,-2), vec(-1,0,0), vec(1,0,0) ] circpath = paths.circle(radius=3) rectpath = paths.rectangle(width=4, height=2) A path need not be closed, in which case there will be end caps. For example, the following path is a portion of a circle: arcpath = paths.arc(angle1=pi/4, angle2=pi) 3) Create an extrusion object to extrude your shape along your path. For example, using paths and shapes defined above, plus a color specification, extrusion(pos=circpath, shape=rect, color=color.red) Note that you can include attributes such as color, size, axis, up, and opacity when creating the extrusion. Point positions are relative: A point whose pos is vector(2, 1, 0) is of course normally displayed at location vector(2, 1, 0). However, the position of a point is relative to an extrusion's own origin value, which by default is vector(0, 0, 0). If you change the extrusion's origin value to vector(10, 6, 5), the point is displayed at the location vector(12, 7, 5); that is, the point is displayed 2 to the right, 6 above, and 0 in front of the extrusion's position vector(10, 6, 5). Another way of saying this is that the display location is the vector sum, vector(10, 6, 5) + vector(2, 1, 0). This means that you can quickly and efficiently move the entire extrusion just by changing the extrusion's origin value. The pos value of an individual point does not change; it's just that the point is displayed in a shifted position. As a result, moving an entire extrusion is very fast. Path direction The paths in the shapes and paths library go counterclockwise in the xz plane, as seen from above. That is, if starting from a position on the x axis, they head in the -z direction and bend toward the left. If your shape has something sticking out on the right, it will be on the outer side of the extrusion, whereas something sticking out on the left will be on the inner side of the extrusion. However, when specifying a path from the shapes and paths library, you can specify a pos and up, to tip the path out of the x-z plane. The path of the following extrusion will have a center at the location vector(1,2,0), oriented perpendicular to the vector(1,0,0): extrusion(pos=paths.circle(pos=vector(1,2,0), shape=shapes.rectangle(width=0.4, height=0.2), up=vector(1,0,0), radius=2), color=color.cyan) How the extrusion machinery works At every point along the pos path this point plus the preceding and following points define a plane. A 2D plane is established perpendicular to the tangent to the path at this point. The 2D shape is drawn in this 2D plane. A shape should be positioned so that its center is approximately at the location of the pos locations. If you offset the shape far from the path, you may get odd results, because there is enhanced danger of two adjacent drawing planes intersecting each other. Also, making sharp turns of wide extrusions may lead to one segment overlapping another. If the bending angle from one point to the next is large, a mitered joint is produced. The bending angle is considered to be large if its cosine is greater than 0.95 (an angle of less than about 18 degrees). Holes in the 2D shape You can create a 2D shape with holes in it, in which case the extrusion has hollow sections. The statement below creates an extrusion of a circular disk that contains a triangular hole and a trapezoidal hole: extrusion(pos=[vec(0,0,0), vec(0,0,-5)], color=color.orange, shape=[ shapes.circle(radius=3), shapes.triangle(length=2), shapes.trapezoid(pos=[0,2], width=4, height=1, top=2) ]) Here the shape is described by a list of shapes. The first shape in the list is always the outer contour, and the remaining shapes represent holes. Holes must not overlap each other, which gives an error. It is even possible to have several (non-overlapping) outer contours, each with holes. Suppose "O" represents an outer contour and "I" represents an inner contour (a hole). The following shape has three pieces, two of them with holes: s =[ [O, I, I], [O], [O, I] ] As an example of this, the statement below creates an extrusion of a triangle and a rectangle, and the triangle contains two holes: extrusion(pos=paths.arc(radius=2, angle1=-pi/3, angle2=pi+pi/3), color=color.cyan, shape=[ [shapes.triangle(length=2), shapes.circle(pos=[0,.5], radius=0.2), shapes.trapezoid(pos=[0,-0.2], width=0.6, height=0.4)], [shapes.rectangle(pos=[0,1.8], width=1,height=0.3)] ])