approximated-curve

3D Vector. The given parameter evaluated on the second derivative curve of this curve. Note that this is only valid if this curve has degree of at least two (2), and will throw an error otherwise.

:arguments (parameter "Number. The desired parameter to be evaluated on the second derivative curve.")

Number. This should reflect the actual tolerance achieved with the approximation. In the case of smlib, it is not clear exactly what this value is supposed to mean -- from examples we have seen so far, the value appears to range between 0.0 and 1.0, and it appears that values close to 1.0 indicate a close approximation, and values close to 0.0 indicate a loose approximation..

GDL Instance. In an element of a sequence, this is the container object which holds all elements.

List of Symbols. Lists all the superclasses of the type of this object.

3D Vector. Returns the vector pointing in the positive direction of the specified axis of this object's reference box. :arguments (axis "Keyword. One of the standard axis keywords: :lateral, :longitudinal, :vertical.")

List of 3D points, List of numbers, List of numbers, and integer. Returns four values which are the control points, the weights, the knots, and the degree of the curve.

GDL object of type Box. A box representing the bounding-box.

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 Curve. Specify this if you want this curve to be a clone of an existing curve. (note - this uses a shared underlying curve object, it does not make a copy)

3D Point. Indicates in global coordinates where the center of the reference box of this object should be located.

Either T or a plist of numbers with keys :distance, angle, :length.

:&key ((3d-tolerance 3d-tolerance-default) "Allowed maximum distance between curve segments." (angle-tolerance *angle-tolerance-default) "Allowed maximum angle in radians between end/start tangents of curve segments." (minimum-segment-length minimum-segment-length-default) "Allowed minimum curve segment length.")

List of GDL Instances. All objects from the :objects specification, including elements of sequences as flat lists.

List of GDL Instances. All objects from the :objects specification, including elements of sequences as flat lists.

Keyword symbol, :closed, :open, or :continuous. :continuous if ends are within 3d-tolerance-default and tangents are within angle-tolerance-default, :closed if ends are within 3d-tolerance-default but tangents are not within angle-tolerance-default, and :open if ends are not within 3d-tolerance-default.

Vector of three real numbers. The RGB color of this object as imported from an external format (e.g. IGES) or as specified in :display-controls. Defaults to the foreground color specified in colors-default. This message should not normally be overridden in user application code.

Number. The reciprocal of the radius of curvature at the given parameter.

GDL Curve object. The curve to be approximated with this curve.

Surface Point. First point of intersection between this curve and the other curve given as the argument.

This function also returns a second value, which is a surface point representing the end of a contiguous segment, if any, associated with the surface point given as the primary return value. A NIL value as this second return value indicates that there was no contiguous segment, only an intersecting point as indicated by the surface point given as the primary return value.

:arguments (other-curve "GDL Curve. The curve with which to intersect.") :&key ((distance-tolerance 3d-tolerance-default) "Number. Distance for two points to be considered coincident.") :note use get-parameter-of and get-3d-point-of to extract components of a surface point.

Surface Points. Points of intersection between this curve and another curve.

This function also returns a second value, which is a list of surface points representing the ends of contiguous segments, if any, associated with the surface point in the same position in the primary returned list. NIL values in this second returned list indicate that there was no contiguous segment, only an intersecting point as indicated by the surface point in the primary returned list.

:arguments (other-curve "GDL Curve. The curve with which to intersect.") :&key ((distance-tolerance 3d-tolerance-default) "Number. Distance for two points to be considered coincident.") :note use get-parameter-of, get-3d-point-of, and get-uv-point-of to extract components of a surface point.

List of Symbols. Lists the direct superclasses of the type of this object.

3D Vector. The direction pointing from the start to the end.

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.

Plist. Returns the :documentation plist which has been specified the specific part type of this instance.

List of Plists. The returned list of plists contains information about the points where the tangents of this curve and those of the curve given as the argument are equal.

:arguments (curve "GDL Curve object")

Surface Point. Given a 3D point, returns the point(s) projected normally onto the curve.

:&key ((distance-tolerance [covers entire curve]) "Number. The 3D point must be within this distance of the curve for a successful drop.")

3D Point. Returns the center of the requested edge of this object's reference box. :arguments (direction-1 "Keyword. One of the standard direction keywords: :right, :left, :rear, :front, :top, :bottom." direction-2 "Keyword. A standard direction keyword orthogonal to direction-1.")

3D Point. The point returned by evaluating the curve function at u2.

List of Numbers. Returns the specified number of parameters equally spaced along the curve.

:arguments (number "Number. How many parameters to return.")

:&key ((spacing :arc-length) "Keyword Symbol, :parametric or :arc-length. :arc-length is the default")

List of 3D Points. Returns the specified number of points equally spaced along the curve.

:arguments (number "Number. How many points to return.")

:&key ((spacing :arc-length) "Keyword Symbol, :parametric or :arc-length. Defaults to :arc-length." (arc-length-approximation-tolerance zero-epsilon) "Number. A smaller number gives tighter arc length approximation. Scaled to curve exent.")

3D Point. Returns the center of the requested face (the requested face with respect to the wrt argument if present, or self if wrt is nil) of this object's reference box. :arguments (direction "Keyword. One of the standard direction keywords: :right, :left, :rear, :front, :top, :bottom.")

(wrt "GDL object instance. Reference object for axes")

3D Vector. Returns the vector pointing from this object's reference box center to its requested face-center. :arguments (direction "Keyword. One of the standard direction keywords: :right, :left, :rear, :front, :top, :bottom.")

List of four 3D points. Returns the vertices of the indicated face.

:arguments (direction "Direction keyword, e.g. :top, :bottom etc. Indicates for which face to return the vertices.")

GDL Curve. The first derivative of this curve. The degree will be one less than the degree of this curve.

Boolean. For elements of sequences, T iff there is no previous element.

GDL Instance. Using this instance as the root, follow the reference chain represented by the given path. :arguments (path "List of Symbols or Pairs of Symbol and Integer")

3D-point. This function returns the point given in global coordinates, into relative local coordinates, based on the orientation and center of the object to which the global-to-local message is sent.

:arguments (point "3D-point. The point to be converted to local coordinates")

:examples Please see the examples area.

Number. Z-axis dimension of the reference box. Defaults to zero.

List of GDL Instances. All objects from the :hidden-objects specification, including elements of sequences as flat lists.

Boolean. Indicates whether the object should effectively be a hidden-object even if specified in :objects. Default is nil.

Integer. Synonym for the layer.

Pathname or string. Points to a pre-existing image file to be displayed instead of actual geometry for this object. Defaults to nil

Boolean. Returns non-nil if the given point is in halfspace defined by the plane given a point and direction.

:arguments (point "3D point. a point in the plane" direction "3D vector. The normal of the plane")

Boolean. Given a point and a vector defining a plane, returns T or NIL depending whether this curve lies in the plane. Also returns a second value which is the maximum distance of the curve from the plane.

:arguments (plane-point "3d-point. Point on the plane"
            plane-normal "3d-vector. Normal vector of the plane")
:&key ((distance-tolerance *3d-tolerance-default*) "Number. Allowed distance of any point on the curve from the plane.")

Integer. Sequential index number for elements of a sequence, NIL for singular objects.

Boolean. For elements of sequences, T iff there is no next element.

Integer. The primary IGES-compatible level (layer) on which this object resides. Defaults to the first of the levels. This slot can be overridden in user code to specify a new layer which will be written out when this object is exported with the IGES output-format.

Boolean. T if this object has no children, NIL otherwise.

List of GDL Objects. A Collection of the leaf nodes of the given object.

List of GDL Objects. A Collection of the leaf nodes of the given object.

Number. Y-axis dimension of the reference box. Defaults to zero.

List of integers. The IGES-compatible levels (layers) on which this object resides. GDL does not currently support writing out multiple levels (layers) through the IGES writer ; only the first of these will be output if the object is exported with the IGES output-format (please contact Genworks if you need all levels (layers) to be written out).

List of 3D points. Returns the points of intersection between given line and the reference box of this object.

:arguments (p-line "3D point. A point in the line" u-line "3D vector. The direction vector of the line")

GDL object of type Box. A box representing the local-box.

Returns a bbox object, answering xmin, ymin, zmin, xmax, ymax, and zmax, for a box containing the convex hull (i.e. the control points) of this curve and oriented according to the given center and orientation.

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.

3D Point. The center of this object, from the perspective of the parent. Starting from the parent's center and using the parent's orientation, this is the relative center of this object.

3D Point. The center of this object, from the perspective of the parent. Starting from the parent's center and using the parent's orientation, this is the relative center of this object.

3x3 Matrix of Double-Float Numbers. Indicates the local Rotation Matrix used to create the coordinate system of this object. This is the "local" orientation with respect to the parent. Multiplying the parent's orientation with this matrix will always result in the absolute orientation for this part.

:note An orientation of NIL indicates the 3x3 identity matrix.

3D-point. This function returns the point given in relative local coordinates, converted into global coordinates, based on the orientation and center of the object to which the local-to-global message is sent.

:arguments (point "3D-point. The local point to be converted to global coordinates")

:examples Please see the examples area.

Boolean. Indicates whether the new-curve should contain matching parameterization between breakpoints. If nil, the parameterization can slip a little, but not very much. Allowing the parameterization between breakpoints to slip results in somewhat fewer control points. Use non-nil only if a parameter-to-parameter match is important to your application. The default is nil.

Plist. The returned plist contains information about the maximum distance from this curve to the curve given as the argument.

:arguments (curve "GDL Curve object")

Plist. The returned plist contains information about the maximum distance from this curve to the point given as the argument.

:arguments (point "3D Point")

String. This is synonymous with slot-documentation

List of Keyword Symbols. Returns the messages (slots, objects, and functions) of this object, according to the filtering criteria as specified by the arguments. :&key ((category :all) "Keyword. Either :all or the individual category of messages to be returned. This can be one of:

• :computed-slots

• :settable-computed-slots

• :required-input-slots

• :optional-input-slots

• :defaulted-input-slots

• :query-slots

• :functions

• :objects

• :quantified-objects

• :hidden-objects

• :quantified-hidden-objects

" (message-type :global) "Keyword Symbol, :local or :global. Indicates whether to return messages only from the local specific part type, or from all superclasses (mixins) as well." (return-category? nil) "Boolean. Indicates whether or not the category of each message should be returned before each message in the returned list." (base-part-type nil) "Symbol naming a GDL Part Type. Indicates a "base" part from which no messages should be returned, nor should messages be returned from superclasses (mixins) of this base part. If NIL (the default), messages are considered from all superclasses." (sort-order :unsorted) "Keyword Symbol. One of: :unsorted, :by-category, or :by-name." (filter :normal) "Function Object of two arguments or :normal. If a function object, applies this function to each returned category and message keyword, and filters out all pairs for which the function returns NIL. If :normal (the default), then no filtering is done.")

Plist. The returned plist contains information about the minimum distance from this curve to the curve given as the argument.

:arguments (curve "GDL Curve object")

Plist. The returned plist contains information about the minimum distance from this curve to the point given as the argument.

:arguments (point "3D Point")

Number. The minimum radius of curvature for the curve. A second value is also returned, which is a surface point indicating the point on the curve where this minimum radius occurs. A third value is also returned, which is a list of additional curve parameters where similar minimum radii occur.

List of Symbols. Returns the names of the immediate superclasses of this object.

:&key ((local? t) "Boolean. Indicates whether to give only direct mixins or all mixins from the entire inheritance hierarchy.")

Keyword symbol. The part's simple name, derived from its object specification in the parent or from the type name if this is the root instance.

GDL Instance. For elements of sequences, returns the next part in the sequence.

3D Vector. The normal of the curve at the given parameter value, i.e. the vector pointing from the point on the curve at this parameter to the center of the osculating circle at that point. if the curve has no curvature at the given parameter, NIL is returned.

:arguments (parameter "Number. The desired parameter to be evaluated on the curve.")

3x3 Orthonormal Matrix of Double-Float Numbers. This is synonymous with the orientation.

Surface point. Returns point at given parameter offset by given distance.

:arguments (curve-parameter "Number. The curve parameter to start from" distance "Number. The distance to offset")

List of GDL surfaces. The surfaces on which this curve lies.

Boolean. Returns non-NIL if the given parameter lies within the parameter range of this curve.

:arguments (parameter "Number. The parameter to be tested.")

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 may or may not support this functionality (see viewport-html-div).

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).

Number. Returns the parameter representing a point offset from the start of the curve by the given length.

:arguments (distance "Number. The arc length from the start.")

Number. Returns the parameter of the given point on the curve. :arguments (point "Point. The point of which the parameter should be calculated.")

Numbers (multiple return values). The minimum and maximum parameter values for this parametric curve.

GDL Instance. The parent of this object, or NIL if this is the root object.

List of numbers. These are parameter values from the original curve where the approximated curve will be forced to be identical to the original curve. Defaults to nil.

Surface Point. First point of intersection between this curve and the plane denoted by plane-point and plane-normal

:note use get-parameter-of and get-3d-point-of to extract components of a surface point.

Surface Points. Points of intersection between this curve and the plane denoted by plane-point and plane-normal.

:note use get-parameter-of and get-3d-point-of to extract components of a surface point.

3D Point. The point on the curve corresponding to the given parameter value.

:arguments (parameter "Number. The desired parameter to be evaluated on the curve.")

GDL Instance. For elements of sequences, returns the previous part in the sequence.

Number. The radius of curvature (i.e. radius of the osculating circle) at the given parameter.

:arguments (parameter "Number. The parameter at which to compute radius of curvature")

Void. Restores all settable-slots in this instance to their default values.

Multiple Values: Total root-paths affected and total slots affected. Reverts any "remembered" bashed slots, starting from the root, to their default values. Note that any call to set-slot! or set-slots! or any use of web form-controls will result in "remembered values". Note that there is a :remember? keyword argument to set-slot! which defaults to t but if you specify it as nil, you can bash values without having them "remembered" and such slots would not be affected by this function.

NIL. Restores the value of the given slot to its default, thus "undoing" any forcibly set value in the slot. Any dependent slots in the tree will respond accordingly when they are next demanded. Note that the slot must be specified as a keyword symbol (i.e. prepended with a colon (":")), otherwise it will be evaluated as a variable according to normal Lisp functional evaluation rules. :arguments (slot "Keyword Symbol") :key (force? "Boolean. Specify as t if you want to force non-settable slots to recompute (e.g. reading from databases or external files). Defaults to nil.")

nil. Restores the value of the given slots to their defaults, thus "undoing" any forcibly set values in the slots. Any dependent slots in the tree will respond accordingly when they are next demanded. Note that the slots must be specified as keyword symbols (i.e. prepended with colons (":")), otherwise they will be evaluated as variables according to normal Lisp functional evaluation rules.

:arguments (slots "List of Keyword Symbols")

:&key ((force? force-restore-slot-default?) "Boolean. Indicates whether the slot values should be unbound, regardless of whether it had actually been bashed previously.")

Void. Restores all settable-slots in this instance, and recursively in all descendant instances, to their default values.

GDL Instance. The root-level node in this object's "tree" (instance hierarchy).

List of Symbols or of Pairs of Symbol and Integer. Indicates the path through the instance hierarchy from the root to this object. Can be used in conjunction with the follow-root-path GDL function to return the actual instance.

List of Symbols or of Pairs of Symbol and Integer. Indicates the path through the instance hierarchy from the local root to this object. Can be used in conjunction with the follow-root-path GDL function to return the actual instance.

Boolean. T iff this part has NIL as its parent and therefore is the root node.

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

List of GDL Instances. All objects from the :hidden-objects specification, including elements of sequences as flat lists. Any children which throw errors come back as a plist with error information

GDL Curve. The second derivative of this curve. The degree will be two less than the degree of this curve.

NIL. Forcibly sets the value of the given slot to the given value. The slot must be defined as :settable for this to work properly. Any dependent slots in the tree will respond accordingly when they are next demanded. Note that the slot must be specified as a keyword symbol (i.e. prepended with a colon (":")), otherwise it will be evaluated as a variable according to normal Lisp functional evaluation rules.

Note also that this must not be called (either directly or indirectly) from within the body of a Gendl computed-slot. The caching and dependency tracking mechanism in Gendl will not work properly if this is called from the body of a computed-slot, and furthermore a runtime error will be generated.

:arguments (slot "Keyword Symbol" value "Lisp Object. (e.g. Number, String, List, etc.)")

:&key ((remember? t) "Boolean. Determines whether to save in current version-tree." (warn-on-non-toplevel? t) "Boolean. Determines whether to warn if this is called from the body of a cached slot." )

NIL. Forcibly sets the value of the given slots to the given values. The slots must be defined as :settable for this to work properly. Any dependent slots in the tree will respond accordingly when they are next demanded. Note that the slots must be specified as a keyword symbols (i.e. prepended with a colon (":")), otherwise they will be evaluated as variables according to normal Lisp functional evaluation rules. :arguments (slots-and-values "Plist. Contains alternating slots and values to which they are to be set." warn-on-non-toplevel? "Boolean. Indicates whether a warning should be issued for calling from inside the body of a cached slot. Default is t.")

Plist of Symbols and Strings. Returns the part types and slot documentation which has been specified for the given slot, from most specific to least specific in the CLOS inheritance order. Note that the slot must be specified as a keyword symbol (i.e. prepended with a colon (":")), otherwise it will be evaluated as a variable according to normal Lisp functional evaluation rules. :arguments (slot "Keyword Symbol. Names the slot for which documentation is being requested.")

Body of GDL code, in list form.

:arguments (slot "Keyword Symbol. Names the slot for which documentation is being requested.")

Keyword symbol. Describes the current status of the requested slot:

• :unbound: it has never been demanded.

• :invalidated: it was demanded at some point, but something it depends on has been modified since; it is currently unbound and will be re-evaluated on next demand.

• :evaluated: it has been demanded and it is currently bound to the default value based on the code.

• :set: (for :settable slots only, which includes all required :input-slots) it has been modified and is currently bound to the value to which it was explicitly set.

• :toplevel: (for root-level object only) its value was passed into the root-level object as a toplevel input at the time of object instantiation.

3D Point. The point returned by evaluating the curve function at u1.

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.

Boolean. This will be t if the curve is generated successfully, nil otherwise.

Surface point. Returns the first point of intersection between this curve and the surface given as an argument.

:arguments (surface "GDL Surface object. The surface to intersect with this curve.") :&key ((3d-tolerance 3d-tolerance-default) "Number. The tolerance to use for intersecting.")

List of Surface points. Returns the point(s) of intersection between this curve and the surface given as an argument.

:arguments (surface "GDL Surface object. The surface to intersect with this curve.") :&key ((3d-tolerance 3d-tolerance-default) "Number. The tolerance to use for intersecting.")

3D Vector. The curve tangent at the given parameter value. Supplementary values returned are: the 3D point at the parameter value. If keyword argument :include-curvature? is given as non-NIL, the radius of the osculating circle, the center for the osculating circle, the normal for the osculating circle, and the curve normal are also returned. Note: If :include-curvature? is given as non-NIL and the curve has no curvature at the specified parameter, NIL is returned for each of these four values.

:arguments (parameter "Number. The desired parameter to be evaluated on the curve.") :&key ((include-curvature? nil) "Boolean (T or NIL). Indicates whether to compute curvature information.")

List of Plists. The returned list of plists contains information about the points where the tangents of this curve and the vector given as the argument are equal.

:arguments (vector "GDL Vector")

Void. Sets giving slot to its boolean opposite. &args (slot "Keyword symbol. Name of the slot as a keyword symbol.")

Number. The maximum distance deviation from the curve-in to this curve. Defaults to 1.0e-5 times the diagonal of the bounding box of the input curve.

Number. The total length of the curve from given start-parameter to given end-parameter.

:&key ((u1 (the u1)) "Number. The start parameter for computing the length" (u2 (the u2)) "Number. The end parameter for computing the length" (tolerance 0.01) "Number. The tolerance (absolute or relative to curve extent) for computing the length" (tolerance-type :relative) "Keyword Symbol, :relative or :absolute. The type of the specified tolerance")

GDL Curve object. Returns a curve which is trimmed from parameter-1 to parameter-2.

:arguments (parameter-1 "Number. The start parameter" parameter-2 "Number. The end parameter")

Symbol. The GDL Type of this object.

Number. The highest parameter value of the underlying mathematical definition for this parametric curve

Number. The lowest parameter value of the underlying mathematical definition for this parametric curve

Number. Equal to the natural u-min of the curve.

Number. Equal to the natural u-max of the curve.

Void. Uncaches all cached data in slots and objects throughout the instance tree from this node, forcing all code to run again the next time values are demanded. This is useful for updating an existing model or part of an existing model after making changes and recompiling/reloading the code of the underlying definitions. Any set (modified) slot values will, however, be preserved by the update.

GDL Curve object. The corresponding UV curve for the primary surface on which this curve lies, if any. If this is not a surface-curve, this will return an error.

3D Point. Returns the center of the requested vertex (corner) of this object's reference box. :arguments (direction-1 "Keyword. One of the standard direction keywords: :right, :left, :rear, :front, :top, :bottom." direction-2 "Keyword. A standard direction keyword orthogonal to direction-1." direction-3 "Keyword. A standard direction keyword orthogonal to direction-1 and direction-2.")

List of GDL Instances. Additional objects to display in Tatu tree. Typically this would be a subset of hidden-children. Defaults to NIL.

Number. X-axis dimension of the reference box. Defaults to zero.

Void. Writes a file containing the toplevel inputs and modified settable-slots starting from the root of the current instance. Typically this file can be read back into the system using the read-snapshot function.

:&key ((filename "/tmp/snap.gdl") "String or pathname. The target file to be written." (root-paths-to-ignore nil) "List of root-paths or nil. Any objects with matching root-path will be ignored for the snapshot write." )