Classes
point n
| Geometry suite |
| This suite defines the requested properties for geometric objects. A geometric object here is actually an AppleScript's record. |
transformation n : a list of 6 real numbers {a, b, c, d, tx, ty}. Any point will undergo the mapping: {x, y} -> {ax + cy + tx, bx + dy + ty}. The Identity transformation is {1, 0, 0, 1, 0, 0}
straight line n
properties
point list of real : coordinates of the origin
angle real : the orientation in radians
limits list of real : optional field {xmin,xmax}. If the field is present, geompath draws the line from abscissa xmin thru abscissa xmax; abscissa 0 is "point"
line segment n
properties
point list of real : coordinates of the origin
endpoint point : coordinates of the endpoint
limits list of real : optional field {xmin,xmax}. If the field is present, geompath draws the line segment from abscissa xmin thru abscissa xmax; abscissa 0 is "point" and abscissa 1 is "endpoint"
circle n : a circle
properties
point list of real : coordinates of the center
radius real
limits list of real : optional field {amin,amax}. If the field is present, geompath draws an arc from angle amin to amax, counter-clockwise; angle 0 corresponds to horizontal axis
ellipse n : an ellipse. To create an ellipse, use "create ellipse" to create an ellipse or apply a transformation to a circle
properties
point list of real : coordinates of the center
radius real
transformation list of real : a 2 by 2 matrix m. m is symmetric and has determinant 1. The ellipse is the image of a circle of radius "radius" thru the transformation defined by m and the center
limits list of real : optional field (see circle)
| Transformations |
apply v : apply a transformation to a geometric object or to a transformation
apply transformation
to any : a geometric object, a point or a transformation
→ record : or transformation
symmetry v : create (or apply) a symmetry
symmetry [record] : a point, a straight line, a circle..., or list
about any : point or straight line
→ any : a transformation if the direct parameter is missing, else the transformed direct parameter
rotate v : create (or apply) a rotation
rotate [record] : a point, a straight line, a circle..., or list
[thru real] : angle in radians
[about point] : the fixed point (default {0,0})
→ any : a transformation if the direct parameter is missing, else the transformed direct parameter
homothecy v : create (or apply) a homothecy
homothecy [record] : a point, a straight line, a circle..., or list
ratio real : similitude ratio
[about point] : the fixed point (default {0,0})
→ any : a transformation if the direct parameter is missing, else the transformed direct parameter
similarity v : create (or apply) a similarity
similarity [record] : a point, a straight line, a circle..., or list
[thru real] : angle in radians
ratio real : similitude ratio
[about point] : the fixed point (default {0,0})
→ any : a transformation if the direct parameter is missing, else the transformed direct parameter
translate v : create (or apply) a translation
translate [record] : a point, a straight line, a circle..., or list
thru point : translation vector
→ any : a transformation if the direct parameter is missing, else the transformed direct parameter
inverse transformation of v : create the inverse transformation
inverse transformation of transformation
| Constructions |
line from v : create a straight line (an AppleScript's record) from a pair of points
line from list of point : 2 points or a line segment
create point on v
create point on straight line : or line segment or circle
at real : the abscissa of the point on the line (in the line segment units if the direct parameter is a line segment) or the angle of the vector from the center to the desired point if the direct parameter is a circle
→ point
create ellipse v
bisector v
bisector list of point : 3 points. {A, O, A'} to get the bisector thru O of the angle AOA'
→ straight line : the bisector with O as point property
perpendicular bisector v
perpendicular bisector list of point : 2 points or a line segment
→ straight line : perpendicular bisector with middle of direct parameter as point property
perpendicular to v
parallel to v
project v
intersect v
intersect list of record : a list of 2 objects: straight lines, circles or ellipses
→ list of point : or empty list
distance from v
distance from any : geometric object
to any : another geometric object
→ real
nearby points from v
nearby points from any : geometric object
to any : another geometric object
→ list of point : a list of two points. The first one belongs to the direct parameter and the second one to the "to" parameter
| Drawings |
geompath v : draw a geometric object. If the object has a property "limits" (as a list of 2 real numbers), geompath will use it
geompath record : a straight line, a line segment or a circle.
markpoint v : mark a point with a small tick
markpoint point : or a real: the abscissa of the point on the line
on straight line : or a line segment
magnitude real : length of the tick in pixels
markrightangle v : mark a right angle with a square
markrightangle list of point : a list of 3 points defining the right angle
magnitude real : size of the square in pixels
markangle v : mark an angle with small arcs
markangle list of point : a list of 3 points defining the angle to mark
magnitude real : size of the smallest radius in pixels
[narcs integer] : number of arcs. Default 1