GendL Application - BEZIER-CURVE

Object: BEZIER-CURVE (The :GEOM-BASE Package)

Description

GDL currently supports third-degree Bezier curves, which are defined using four 3D control-points. The Bezier curve always passes through the first and last control points and lies within the convex hull of the control points. At the start point (i.e. the first control point), the curve is tangent to the vector pointing from the start point to the second control point. At the end point (i.e. the last control point), the curve is tangent to the vector pointing from the end point to the third control point.

Input Slots (required)

CONTROL-POINTS list of 4 3d points
Specifies the control points for the Bezier curve.

Input Slots (optional)

HIDDEN? [from VANILLA-MIXIN] boolean*
Indicates whether the object should effectively be a hidden-object even if specified in :objects. Default is nil.

IMAGE-FILE [from BASE-OBJECT] pathname or string
Points to a pre-existing image file to be displayed instead of actual geometry for this object. Defaults to nil

LOCAL-BOX [from BASE-OBJECT] list of two 3d points
The left front bottom and right rear top corners, in global coordinates, of the rectangular volume bounding this geometric object.

OBLIQUENESS [from BASE-OBJECT] 3x3 orthonormal matrix of double-float numbers
This is synonymous with the `orientation`.

ONCLICK-FUNCTION [from BASE-OBJECT] lambda function of zero arguments, or nil
If non-nil, this function gets invoked when the user clicks the object in graphics front-ends which support this functionality, e.g. SVG/Raphael and X3DOM.

ROOT [from VANILLA-MIXIN] gdl instance*
The root-level node in this object's ``tree'' (instance hierarchy).

SAFE-CHILDREN [from VANILLA-MIXIN] list of gdl instances*
All objects from the :objects specification, including elements of sequences as flat lists. Any children which throw errors come back as a plist with error information

STRINGS-FOR-DISPLAY [from VANILLA-MIXIN] string or list of strings*
Determines how the name of objects of this type will be printed in most places. This defaults to the name-for-display (generally the part's name as specified in its parent), followed by an index number if the part is an element of a sequence.

VISIBLE-CHILDREN [from VANILLA-MIXIN] list of gdl instances*
Additional objects to display in Tatu tree. Typically this would be a subset of hidden-children. Defaults to NIL.

Input Slots (optional, defaulting)

CENTER [from BASE-OBJECT] 3d point
Indicates in global coordinates where the center of the reference box of this object should be located.

DISPLAY-CONTROLS [from BASE-OBJECT] plist
May contain keywords and values indicating display characteristics for this object. The following keywords are recognized currently: :color color keyword from the color-table parameter, or an HTML-style hexidecimal RGB string value, e.g. "#FFFFFF" for pure white. Defaults to :black. :line-thickness an integer, defaulting to 1, indicating relative line thickness for wireframe representations of this object. :dash-pattern (currently PDF/PNG/JPEG only). This is a list of two or three numbers which indicate the length, in pixels, of the dashes and blank spaces in a dashed line. The optional third number indicates how far into the line or curve to start the dash pattern.

HEIGHT [from BASE-OBJECT] number
Z-axis dimension of the reference box. Defaults to zero.

LENGTH [from BASE-OBJECT] number
Y-axis dimension of the reference box. Defaults to zero.

ORIENTATION [from BASE-OBJECT] 3x3 matrix of double-float numbers
Indicates the absolute Rotation Matrix used to create the coordinate system of this object. This matrix is given in absolute terms (i.e. with respect to the root's orientation), and is generally created with the alignment function. It should be an orthonormal matrix, meaning each row is a vector with a magnitude of one (1.0).

WIDTH [from BASE-OBJECT] number
X-axis dimension of the reference box. Defaults to zero.

Computed Slots

BOUNDING-BOX [from BASE-OBJECT] list of two 3d points
The left front bottom and right rear top corners, in global coordinates, of the rectangular volume bounding the tree of geometric objects rooted at this object.

GDL Functions

CIRCLE-INTERSECTION-2D list of 3d points
Returns points of intersection in the Z plane between this Bezier curve and the circle in the Z plane with center `center` and radius `radius`. arguments: center 3D Point The center of the circle to be intersected radius Number The radius of the circle to be intersected keyword arguments: accuracy Number, Default Value: `(* 10.0 DOUBLE-FLOAT-EPSILON)` Target accuracy maximum-number-of-iterations Integer, Default Value: `30` Maximum iterations of polynomial solver

LINE-INTERSECTION-2D list of 3d points
Returns points of intersection in the Z plane between this Bezier curve and the infinite line containing point `point` and direction `vector`. Use the between? function if you wish to establish whether the point is contained in a particular line segment. arguments: point 3D Point Any point in the line to be intersected vector 3D Vector The direction of the line to be intersected keyword arguments: accuracy Number, Default Value: `(* 10.0 DOUBLE-FLOAT-EPSILON)` Target accuracy maximum-number-of-iterations Integer, Default Value: `30` Maximum iterations of polynomial solver

POINT 3d point
Returns the point on this Bezier curve corresponding to the given `parameter`, which should be between 0 and 1. arguments: parameter Number Curve parameter, between zero and one (0 and 1)

Examples

 (in-package :gdl-user)

 (define-object bezier-sample (bezier-curve)
  :computed-slots
  ((control-points (list (make-point 0 0 0)
                         (make-point 1 1 0)
                         (make-point 2 1 0)
                         (make-point 3 0 0))))
  :objects
  ((points-display :type 'points-display
                   :points (the control-points))))

 (generate-sample-drawing :objects (let ((self (make-object 'bezier-sample)))
                                     (list self (the points-display))))

Package Documentation