ApasScript.

3d Pictures

3D pictures

space3d

Starts a picture of 3D space, drawn in perspective and turned so the axes read as in the textbook: z up, x towards you, y to the right. Add to it with axes3d, point3d, segment3d, arrow3d, face3d, plane3d, angle3d and label3d; turn it with view3d.

axes3d

Draws the x, y and z axes as labelled arrows from the origin O, their negative halves dashed.

point3d

Marks a point with a dot and, if given, its name beside it.

segment3d

Draws the straight line from p to q, solid or dashed (for a perpendicular or a projection).

arrow3d

Draws a vector as an arrow from one point to another, its head a cone drawn as it is seen, with an optional name at the tip.

face3d

Draws a flat polygon through three or more points in order, shaded by how it faces the light. A colour and an opacity may follow the points.

plane3d

Draws a square piece of the plane through a point with a given normal, see-through so what is behind shows.

angle3d

Marks the angle p-at-q with an arc at `at` and writes its size in degrees, measured from the points, unless a label is given.

label3d

Writes text at a point in space.

view3d

Turns the camera: change yaw from frame to frame to spin the picture round the vertical axis.

curve3dOn

Draws a curve in space from three formulas in t, for t from t0 to t1: a helix, a wave, a path. Arrowheads along it can show the way it runs. The formulas are kept as written; t is the curve's own and the script's t is left as it was.

revolve3d Apas Cloud

Draws the solid made by turning the region under y = outer(x), for x from a to b, about the x axis (the disc method); with an inner curve, the solid between the two (the washer method), with its hole. The end faces are drawn and the curves turned are marked in red in the xy plane. See-through (opacity 0.45 unless given). Turn the camera with space3d's yaw (75 puts x to the right). An axis may follow (E47): "y = 2" or "x = -1" or "y-axis"; then the curves are y = f(x) (or x = g(y), written in y) and the radii are their distances from that line, which is drawn; give "" for no inner curve before it.

crossSections3d Apas Cloud

Draws a solid with known cross sections: the base region between y = bottom(x) and y = top(x), for x from a to b, in the floor (z = 0), and n slices standing on it across the region at the middles of n equal parts: "square", "semicircle" (its diameter across the base), "equilateral" (triangle) "rectangle" (k times as high as wide), "isosceles-leg" (a right isosceles triangle with a leg on the base) or "isosceles-hypotenuse" (with its hypotenuse on the base).

3D pictures

fieldLines3d

Draws point charges and the electric field lines between them in space, each line with an arrowhead the way the field points (from + to −). The field is the normalised Coulomb field, E = Σ q r/r³; lines leave each positive charge evenly in all directions, as many as per_charge × |q|.

model3d

A molecule in 3D as a ball-and-stick (or space-filling) picture, from its real shape: the built-in set is PubChem's computed 3D conformers, checked against the textbook's bond lengths and angles. Built in: ethane, butane, cyclohexane, ethene, ethyne, benzene, methanol, ethanol, acetic acid, glucose (beta-D-glucopyranose), alanine (L), d-alanine, lactic acid (L), d-lactic acid, glycine, adenine, thymine, guanine, cytosine. Atoms are numbered from 1 as in the molfile. Turn a bond with torsion3d, measure with dihedral3d, mirror with mirror3d, look down a bond with viewAlong3d.

torsion3d

Turns the atoms on j's side of the bond i-j about that bond by the given degrees; bond lengths and angles stay as they are. A bond in a ring is refused.

dihedral3d

The dihedral (torsion) angle a-i-j-b in degrees, between -180 and 180, measured from the positions: 60 is gauche or staggered, 180 anti, 0 eclipsed.

conformation3d

Ethane (H-C-C-H) or butane (C-C-C-C) turned to the given dihedral, with the dihedral and its name (staggered, eclipsed, anti, gauche) written under the picture.

mirror3d

The mirror image of a molecule as a new picture, for chirality: L-alanine and its mirror image (D-alanine) side by side. The original is unchanged.

viewAlong3d

Turns the camera to look from atom i straight down the bond to atom j: the Newman view, in 3D.

dna3d

The B-DNA double helix of a strand and its partner, as in NCERT XII Biology Fig. 5.3: two sugar-phosphate backbones, right-handed, 0.9 nm from the axis; each base pair a bar across, half in each base's colour (adenine yellow, thymine green, guanine orange, cytosine red); A pairs with T and G with C; 0.34 nm and 36° from one pair to the next, so 10 pairs make a 3.4 nm turn. The backbones stand 144° apart across the minor groove, so the major and minor grooves show. 5′ and 3′ mark the ends: the strands run opposite ways. Units are nm, the axis along z.