Quaternion stuff + Breather

e5a382b0-4932-4acd-8441-74066b57a35d 27 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

a 0.5 :

β 1.5 :

# # Solve

Solve("1:expression", "2:expression") - [Maxima] Solve(eqn, var) solves eqn for var. eqn is a boolean equation or a list of equations, var is a variable name or a list of names to solve for. Returns solutions as boolean equations var=value. Multiple solutions are given as a row vector. Use Assign() in order to apply solutions as assignments to var.

Solving this typical Quaternion system is NOT resident in the downloaded SmathStudio 2014_11_16 Maxima 5_34_1. So, you will be "zap" for this one in your work sheet.

C:\Smath+Maxima\2014 11 16 SMath and Maxima\Maxima-5.34.1\bin\maxima.bat

α 0.5 :

β 1 :

p 0.2 :

Quaternion stuff + Breather

1. Given the Quaternion vector system, it has two orthogonal vector solution, of which the symbolic expansion is 'V'.

2. Define some constant term "modulo"

modulo 2 β 2^* 2 β * α * + 2 α 2^* + sqrt :

V β - modulo / β modulo / β α + (modulo / β α + (- modulo / α modulo / α - modulo / 32 mat :

V 0.5345 - 0.5345 0.8018 0.8018 - 0.2673 0.2673 - 32 mat

3. Create the Quaternion vector

q V 1 col p stack :

q 0.5345 - 0.8018 0.2673 0.2 41 mat

4. Define the "UnitV", apply to 'q'

# norme Euclidean norm ≡

q q q norme / :

q that goes in 'quat' converter

q 0.5241 - 0.7862 0.2621 0.1961 41 mat

5. The rotation 'quat' converter

quat 12 q 3 el (2^* - 2 q 4 el (2^* - 2 q 2 el * q 3 el * 2 q 1 el * q 4 el * - 2 q 1 el * q 3 el * 2 q 2 el * q 4 el * + 2 q 1 el * q 4 el * 2 q 2 el * q 3 el * + 12 q 2 el (2^* - 2 q 4 el (2^* - 2 q 1 el * q 2 el * - 2 q 3 el * q 4 el * + 2 q 1 el * q 3 el * - 2 q 4 el * q 2 el * + 2 q 1 el * q 2 el * 2 q 3 el * q 4 el * + 12 q 2 el (2^* - 2 q 3 el (2^* - 33 mat :

γ quat :

ρ 1 b 2^- :

b 0.6 :

w ρ sqrt :

ρ 0.64

u v d b w b u * cosh (2^* b w v * sin * (2^+ (* :

u v f u - 2 ρ * b u * cosh * b u * sinh * u v d / + 2 w * b u * cosh * w v cos * w v * cos * - v sin w v * sin * - (* u v d / 2 w * b u * cosh * w v sin * w v * cos * - v cos w v * sin * - (* u v d / 31 mat :

M u v f 13.2 - 13.2 37.4 - 37.4 2020 CreateMesh eval :

Draw-Descriptions (Maxima) Draw-Descriptions (Maxima)

Optionen

Options

[Maxima Draw] adapt_depth (=10): maximale Teilungstiefe der adaptive Kurvenabtastung [Maxima Draw] adapt_depth (=10) maximum number of adaptive interval splits when drawing curves adapt_depth adapt_depth :

[Maxima Draw] axis_3d (=true): Achsen im 3D zeichnen, false: keine Achsen zeichnen [Maxima Draw] axis_3d (=true): draw 3D axes, false: don't draw axes axis_3d axis_3d :

[Maxima Draw]  axis_bottom (=true): untere Achse im 2D zeichnen, false: Achse nicht zeichnen [Maxima Draw]  axis_bottom (=true): draw bottom axis in 2D, false: don't draw axis axis_bottom axis_bottom :

[Maxima Draw] axis_top (=true): obere Achse im 2D zeichnen, false: Achse nicht zeichnen [Maxima Draw] axis_top (=true): draw top axis in 2D, false: don't draw axis axis_top axis_top :

[Maxima Draw] axis_left (=true): linke Achse im 2D zeichnen, false: Achse nicht zeichnen [Maxima Draw] axis_left (=true): draw left axis in 2D, false: don't draw axis axis_left axis_left :

[Maxima Draw] axis_right (=true): rechte Achse im 2D zeichnen, false: Achse nicht zeichnen [Maxima Draw] axis_right (=true): draw right axis in 2D, false: don't draw axis axis_right axis_right :

[Maxima Draw] background_color (=white): Hintergrundfarbe des Diagramms [Maxima Draw] background_color (=white): background color of the plot background_color background_color :

[Maxima Draw] border (=true): Ränder von polygon(), ellipse() oder rectangle() zeichnen [Maxima Draw] border (=true): draw borders of polygon(), ellipse() or rectangle() objects border border :

[Maxima Draw] cbrange (=auto): Farbbereich (Liste min,max) [Maxima Draw] cbrange (=auto): color bar range (list min,max) cbrange cbrange :

[Maxima Draw] cbtics (=auto): Marken an der Farblegende [Maxima Draw] cbtics (=auto): color bar tick marks cbtics cbtics :

[Maxima Draw] color (=blue): Farbe für Linien, Punkte, Kanten und Text, als Namen oder hexadezimal in der
Form  "#rrggbb" [Maxima Draw] color (=blue): color for lines, points, borders and text, given as name or as "#rrggbb" color color :

[Maxima Draw] colorbox (=true): Farblegende ohne Beschriftung zeichnen, false: keine Farblegende 
zeichnen, text: Farblegende mit text als Beschriftung zeichnen. [Maxima Draw] colorbox (=true): draw color scale without label, false: no colorbar, 
string: draw colorbar with string as label. colorbox colorbox :

[Maxima Draw] contour (=none): Art der Höhenlinien. none: keine, base: auf der xy-Ebene, surface: auf der
3D-Fläche, both: auf xy-Ebene und Fläche, map: auf xy-Ebene und Blickrichtung senkrecht. [Maxima Draw] contour (=none): contour lines. none: no contours, base: on xy plane, surface: on 3D surface, both:
on xy plane and surface, map: on xy plane plus vertical view. contour contour :

[Maxima Draw]  contour_levels (=5): Werte für die Höhenlinien. Anzahl oder Liste  (min, Δ, max), oder
set(L1, L2,...) mit Werten [Maxima Draw]  contour_levels (=5): contour levels. number oder list  (min, Δ, max), or
set(L1, L2,...) of values contour_levels contour_levels :

[Maxima Draw]  data_file_name (="data.gnuplot"): Kurvendaten für Gnuplot [Maxima Draw]  data_file_name (="data.gnuplot"): internal data file name for gnuplot data_file_name data_file_name :

[Maxima Draw]  delay (=5) Zeitschritt in animierten gif-Dateien [Maxima Draw]  delay (=5): time step in animted gif files delay delay :

[Maxima Draw]  dimensions (= 600 x 500): Liste [Breite,Höhe] [Maxima Draw]  dimensions (= 600 x 500) list [width, height] dimensions dimensions :

[Maxima Draw]  draw_realpart (=true) Realteil zur Darstellung komplexer Werte verwenden [Maxima Draw]  draw_realpart (=true) use real part for plotting complex values draw_realpart draw_realpart :

[Maxima Draw]  enhanced3d (=none) Farbpalette, none: 3D Flächen als Gitter zeichnen  
(Steuerung mit color und surface_hide), true: Farbe anhand des z-Werts, 
Liste  [f(x,y,z), x, y, z]: Farbe anhand der Funktion f,  
Liste [f(u,v),u,v]: Farbe anhand der Flächenparameter oder Liste [f(k), k ]: 
Farbe anhand der Punktnummer in points() Objekten [Maxima Draw]  enhanced3d (=none) don't use color palette, draw 3D surfaces as grid 
(control using color und surface_hide), true: coloring of surfaces by z-value, 
or  list  [f(x,y,z), x, y, z]: coloring according to function f or 
list [f(u,v),u,v]  or list [f(k), k ] (k being the point counter in points() objects) enhanced3d enhanced3d :

[Maxima Draw] error_type (=y) Art der Fehlerbalken in errors():  x, y, xy oder boxes [Maxima Draw] error_type (=y) type of error bars in errors():  x, y, xy or boxes error_type error_type :

[Maxima Draw] file_name (="maxima_out") Grafik-Ausgabedatei, Endung wird gemäß Ausgabeformat ergänzt [Maxima Draw] file_name (="maxima_out") output file, extension is set according to format file_name file_name :

[Maxima Draw] fill_color (=red) Füllfarbe für Objejte polygon() und  explicit() in 2D [Maxima Draw] fill_color (=red) fill color for polygons and explicit functions y(x) in 2D fill_color fill_color :

[Maxima Draw] fill_density (=0) Deckungsgrad der Füllfarbe in bars()-Objekten, zwischen 0 und 1 [Maxima Draw] fill_density (=0) opacity of the fill color in bars()-objects, 0..1 fill_density fill_density :

[Maxima Draw] filled_func (=false): explizite Funktionen y(x) werden nicht gefüllt,
true: Füllung bis zur Unterkante des Diagramms, g(x): Füllung zwischen g(x)
 und y(x) [Maxima Draw] filled_func (=false): don't fill explicit functions y(x),
true: fill between the next explicit() object and the bottom border of the diagram, g(x): fill
between g(x) and the next explicit() object filled_func filled_func :

[Maxima Draw] gnuplot_file_name (="maxout.gnuplot"): Kommandodatei für Gnuplot [Maxima Draw] gnuplot_file_name (="maxout.gnuplot"): name of the temporary gnuplot command file gnuplot_file_name gnuplot_file_name :

[Maxima Draw] gnuplot_term (): Ausgabe-Format-Spezifikation (Text nach "set terminal") [Maxima Draw] gnuplot_term (): gnuplot terminal options (arguments of "set terminal") gnuplot_term gnuplot_term :

[Maxima Draw] gnuplot_out_file (=maxplot.xxx) Ausgabedateiname (xxx abhängig vom Format) [Maxima Draw] gnuplot_out_file (=maxplot.xxx) output file name (xxx depends on terminal) gnuplot_out_file gnuplot_out_file :

[Maxima Draw] grid (=false): kein Gitterraster zeichnen, true: Gitter zeichnen [Maxima Draw] grid (=false): don't draw xy grid, true: draw grid grid grid :

[Maxima Draw] head_angle (=45) Pfeilwinkel an vector()-Objekten (halber Öffnungswinkel in °) [Maxima Draw] head_angle (=45): head angle of vector()-Objekten (angle between border and vector 
 direction in °) head_angle head_angle :

[Maxima Draw] head_both (=false) oder true: ob bei vector()-Objekten zwei Pfeilspitzen gezeichnet werden. [Maxima Draw] head_both (=false): don't draw a second head of vector() objects,
 true: draw a second head head_both head_both :

[Maxima Draw] head_length (=2) Länge der Pfeilspitze  bei vector()-Objekten in Einheiten der x-Achse [Maxima Draw] head_length (=2): head length of vector() objects in units of the x-axis head_length head_length :

[Maxima Draw] head_type (=filled) Spitzenform bei vector()-Objekten:  filled, empty  oder nonfilled [Maxima Draw] head_type (=filled) head type of vector() objects:  filled, empty  or nonfilled head_type head_type :

[Maxima Draw] ip_grid (={50, 50): Primäres Gitter für die Darstellung impliziter Funktionen,
als Liste angeben [Maxima Draw] ip_grid (={50, 50): primary grid for sampling of implicit functions, two-element list ip_grid ip_grid :

[Maxima Draw] ip_grid_in (={5, 5 ): Sekundäres Gitter für die Darstellung impliziter Funktionen [Maxima Draw] ip_grid_in (={5, 5 ): secondary grid for sampling of implicit functions ip_grid_in ip_grid_in :

[Maxima Draw] key (=""): Legendeneintrag für das nachfolgende Grafikobjekt. [Maxima Draw] key (=""): legend key for subsequent graphics object. key key :

[Maxima Draw] key_pos (="", entspricht top_right): Legendenposition. Gültige Werte: top_left, top_center, top_right, 
center_left, center, center_right, bottom_left, bottom_center, bottom_right [Maxima Draw] key_pos (="", equivalent to top_right): position of the legend. Valid options: top_left, top_center, top_right, 
center_left, center, center_right, bottom_left, bottom_center, bottom_right key_pos key_pos :

[Maxima Draw] label_alignment (=center), left oder right: horizontale Ausrichtung von Beschriftungen [Maxima Draw] label_alignment (=center), left or right: alignment of text labels label_alignment label_alignment :

[Maxima Draw] label_orientation (=horizontal) oder vertical: Ausrichtung von Texten [Maxima Draw] label_orientation (=horizontal) or vertical: orientation of text labels label_orientation label_orientation :

[Maxima Draw] line_type (=solid) Linienart. Alternativen: dots (für alle Formate) oder wenn von
Gnuplot unterstützt: dashes, short_dashes, short_long_dashes, short_short_long_dashes [Maxima Draw] line_type (=solid) line type. Other options: dots (for all formats) or if supported by
Gnuplot: dashes, short_dashes, short_long_dashes, short_short_long_dashes line_type line_type :

[Maxima Draw] line_width (=1) , >0 line_width line_width :

[Maxima Draw] logcb (=false) oder true: logarithmische Farbskale [Maxima Draw] logcb (=false) or true: log scale of the colorbar logcb logcb :

[Maxima Draw] logx (=false) oder true: logarithmische x-Achse [Maxima Draw] logx (=false) or true: log scale of x-axis logx logx :

[Maxima Draw] logx_secondary (=false) oder true: logarithmische zweite x-Achse [Maxima Draw] logx_secondary (=false) or true: log scale of secondary x-axis logx_secondary logx_secondary :

[Maxima Draw] logy (=false) oder true: logarithmische y-Achse [Maxima Draw] logy (=false) or true: log scale of y-axis logy logy :

[Maxima Draw] logy_secondary (=false) oder true: logarithmische zweite y-Achse [Maxima Draw] logy_secondary (=false) or true: log scale of secondary y-axis logy_secondary logy_secondary :

[Maxima Draw] logz (=false) oder true: logarithmische z-Achse [Maxima Draw] logz (=false) or true: log scale of z-axis logz logz :

[Maxima Draw] nticks (=29): Punktezahl für die Kurvenabtastung [Maxima Draw] nticks (=29): number of points for curve sampling (explicit and parametric) nticks nticks :

[Maxima Draw] palette (=color) Standard-Farbpalette, gray: Graustufen, 
Liste { Farbe1, Farbe2...  oder false: Flächen nicht färben [Maxima Draw] palette (=color) default color palette, gray: gray levels, 
list { color1, color2...  or false: don't color 3D objects palette palette :

[Maxima Draw] point_size (=1) Größe von points()-Symbolen [Maxima Draw] point_size (=1) size of points()-symbols point_size point_size :

[Maxima Draw] point_type (=1) Symbol für points()-Objekte, Name oder Kennzahl: 
none -1, dot 0, plus 1, multiply 2, asterisk 3, square 4, filled_square 5, 
circle 6, filled_circle 7, up_triangle 8, filled_up_triangle 9, down_triangle 10, 
filled_dwn_triangle 11, diamant 12, filled_diamant 13 [Maxima Draw] point_type (=1) type of points() objects, name or key number:
none -1, dot 0, plus 1, multiply 2, asterisk 3, square 4, filled_square 5, 
circle 6, filled_circle 7, up_triangle 8, filled_up_triangle 9, down_triangle 10, 
filled_down_triangle 11, diamant 12, filled_diamant 13 point_type point_type :

[Maxima Draw] points_joined (=false), true or impulses: how to join points() points_joined points_joined :

[Maxima Draw] proportional_axes (=none), xy oder xyz: Achsen mit gleicher Skalierung) [Maxima Draw] proportional_axes (=none), xy or xyz: set axes of equal scaling) proportional_axes proportional_axes :

[Maxima Draw] surface_hide (=false) oder true: Ausblendung verdeckter Flächen bei Linienrasterdarstellung [Maxima Draw] surface_hide (=false) or true: handling of hidden lines in surface grids surface_hide surface_hide :

[Maxima Draw] terminal (=screen) separate interactive terminal window,  png, jpg, gif, eps, svg, pdf, 
animated_gif: gnuplot output format terminal terminal :

[Maxima Draw] title (="") Überschrift für das Diagramm [Maxima Draw] title (="") headline for the plot title title :

[Maxima Draw] transform (=none) Koordinatentransformation, für 2D als Liste {f1(x,y), f2(x,y), x, y, für 3D
als Liste {f1(x,y), f2(x,y), f3(x, y, z), x, y, z [Maxima Draw] transform (=none) co-ordinate transformation, for 2D as list {f1(x,y), f2(x,y), x, y, for 3D
as list {f1(x,y), f2(x,y), f3(x, y, z), x, y, z transform transform :

[Maxima Draw] transparent (=false) oder true: ob Rechtecke, Polygone oder Ellipsen transparent sein sollen 
(bei false werden sie gefüllt) [Maxima Draw] transparent (=false) fill objects with border, true: don't fill (make them transparent) transparent transparent :

[Maxima Draw] tube_extremes (=(open, open) ), open oder closed: Endscheiben von tube()-Objekten. [Maxima Draw] tube_extremes (=(open, open) ), open or closed: how tube() objects are terminated. tube_extremes tube_extremes :

[Maxima Draw] unit_vectors (=false) oder true: Vektoren in originaler Länge oder als Einheitsvektoren zeichnen. [Maxima Draw] unit_vectors (=false) draw vectors in original length, true: draw unit vectors. unit_vectors unit_vectors :

[Maxima Draw] user_preamble (="") Zeichenkette oder Liste von Zeichenketten, die unmittelbar vor dem eigentlichen 
Diagrammbefehl an Gnuplot übergeben werden. [Maxima Draw] user_preamble (="") string or list of strings, gnuplot commands placed  immediately before the plot commands user_preamble user_preamble :

[Maxima Draw] view (=(60,30)) view direction view view :

[Maxima Draw] wired_surface (=false) oder true: Gitternetz auf eingefärbten Flächen anzeigen oder nicht. [Maxima Draw] wired_surface (=false) no grid on colored surfaces, true: draw grid on surfaces wired_surface wired_surface :

[Maxima Draw] x_voxel (=10) x-Bereichsteilung für den  Marching-Cubes-Algorithmus bei implizit gegebenen Flächen [Maxima Draw] x_voxel (=10) number of x steps for the Marching Cube algorithm (for implicit 3D functions) x_voxel x_voxel :

[Maxima Draw] y_voxel (=10) y-Bereichsteilung für den  Marching-Cubes-Algorithmus bei implizit gegebenen Flächen [Maxima Draw] y_voxel (=10) number of y steps for the Marching Cube algorithm (for implicit 3D functions) y_voxel y_voxel :

[Maxima Draw] z_voxel (=10) z-Bereichsteilung für den  Marching-Cubes-Algorithmus bei implizit gegebenen Flächen [Maxima Draw] z_voxel (=10) number of z steps for the Marching Cube algorithm (for implicit 3D functions) z_voxel z_voxel :

[Maxima Draw] xaxis (=false) oder true: Anzeige der x-Achse [Maxima Draw] xaxis (=false) or true: draw x-axis xaxis xaxis :

[Maxima Draw] yaxis (=false) oder true: Anzeige der y-Achse [Maxima Draw] yaxis (=false) or true: draw y-axis yaxis yaxis :

[Maxima Draw] zaxis (=false) oder true: Anzeige der z-Achse [Maxima Draw] zaxis (=false) or true: draw z-axis zaxis zaxis :

[Maxima Draw] xaxis_color (=black) Farbe x-Achse [Maxima Draw] xaxis_color (=black) color of the x-axis xaxis_color xaxis_color :

[Maxima Draw] yaxis_color (=black) Farbe y-Achse [Maxima Draw] yaxis_color (=black) color of the y-axis yaxis_color yaxis_color :

[Maxima Draw] zaxis_color (=black) Farbe z-Achse [Maxima Draw] zaxis_color (=black) color of the z-axis zaxis_color zaxis_color :

[Maxima Draw] xaxis_secondary (=false) oder true: Nutzung einer zweiten x-Achse (oben) für die nachfolgenden Objekte [Maxima Draw] xaxis_secondary (=false) or true: use the secondary x-axis (top) for subsequent objects xaxis_secondary xaxis_secondary :

[Maxima Draw] yaxis_secondary (=false) oder true: Nutzung einer zweiten y-Achse (rechts) für die nachfolgenden Objekte [Maxima Draw] yaxis_secondary (=false) or true: use the secondary y-axis (right) for subsequent objects yaxis_secondary yaxis_secondary :

[Maxima Draw] xaxis_type (=dots) oder solid: Linienart der x-Achse [Maxima Draw] xaxis_type (=dots) or solid xaxis_type xaxis_type :

[Maxima Draw] yaxis_type (=dots) oder solid: Linienart der y-Achse [Maxima Draw] yaxis_type (=dots) or solid yaxis_type yaxis_type :

[Maxima Draw] zaxis_type (=dots) oder solid: Linienart der z-Achse [Maxima Draw] zaxis_type (=dots) or solid zaxis_type zaxis_type :

[Maxima Draw] xaxis_width (=1) Linienbreite der x-Achse [Maxima Draw] xaxis_width (=1) xaxis_width xaxis_width :

[Maxima Draw] yaxis_width (=1) Linienbreite der y-Achse [Maxima Draw] yaxis_width (=1) yaxis_width yaxis_width :

[Maxima Draw] zaxis_width (=1) Linienbreite der z-Achse [Maxima Draw] zaxis_width (=1) zaxis_width zaxis_width :

[Maxima Draw] xlabel (="") x-Achsenbeschriftung [Maxima Draw] xlabel (="") label of the x-axis xlabel xlabel :

[Maxima Draw] ylabel(="") y-Achsenbeschriftung [Maxima Draw] ylabel (="") label of the y-axis ylabel ylabel :

[Maxima Draw] zlabel (="") z-Achsenbeschriftung [Maxima Draw] zlabel (="") label of the z-axis zlabel zlabel :

[Maxima Draw] xrange (=auto) oder Liste {min,max: x-Achsenbereich [Maxima Draw] xrange (=auto) or list {min,max: range of the x-axis xrange xrange :

[Maxima Draw] yrange (=auto) oder Liste {min,max: y-Achsenbereich [Maxima Draw] yrange (=auto) or list {min,max: range of the y-axis yrange yrange :

[Maxima Draw] zrange (=auto) oder Liste {min,max: z-Achsenbereich [Maxima Draw] zrange (=auto) or list {min,max: range of the z-axis zrange zrange :

[Maxima Draw] xrange_secondary (=auto) oder Liste {min,max: Bereich der zweiten (oberen) x-Achse [Maxima Draw] xrange_secondary (=auto) or list {min,max: range of the secondary (top) x-axis xrange_secondary xrange_secondary :

[Maxima Draw] yrange_secondary (=auto) oder Liste {min,max: Bereich der zweiten (rechten) y-Achse [Maxima Draw] yrange_secondary (=auto) or list {min,max: range of the secondary (right) y-axis yrange_secondary yrange_secondary :

[Maxima Draw] xtics (=auto): automatische x-Achsmarken, none: keine, Zahl: Schrittweite, 
Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() 
von Listen ("text",pos) mit Vorgabe von Beschriftung und Position. [Maxima Draw] xtics (=auto): automatic x ticks, none: no x ticks, number: tick interval,  
list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists
("text",pos) for spec of position and text. xtics xtics :

[Maxima Draw] ytics (=auto): automatische y-Achsmarken, none: keine, Zahl: Schrittweite, 
Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() 
von Listen {"text",pos mit Vorgabe von Beschriftung und Position. [Maxima Draw] ytics (=auto): automatic y ticks, none: no y ticks, number: tick interval,  
list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists
("text",pos) for spec of position and text. ytics ytics :

[Maxima Draw] ztics (=auto): automatische z-Achsmarken, none: keine, Zahl: Schrittweite, 
Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() 
von Listen {"text",pos mit Vorgabe von Beschriftung und Position. [Maxima Draw] ztics (=auto): automatic z ticks, none: no x ticks, number: tick interval,  
list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists
("text",pos) for spec of position and text. ztics ztics :

[Maxima Draw] xtics_secondary (=auto): automatische Marken an der sekundären (oberen) x-Achse, none: keine, 
Zahl: Schrittweite, 
Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() 
von Listen {"text",pos mit Vorgabe von Beschriftung und Position. [Maxima Draw] xtics_secondary (=auto): automatic ticks on the secondary (top) x-axis, none: no ticks, number: tick interval,  
list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists
("text",pos) for spec of position and text. xtics_secondary xtics_secondary :

[Maxima Draw] ytics_secondary (=auto): automatische Marken an der sekundären (rechten) y-Achse, none: keine, 
Zahl: Schrittweite, 
Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() 
von Listen {"text",pos mit Vorgabe von Beschriftung und Position. [Maxima Draw] ytics_secondary (=auto): automatic ticks on the secondary (right) y-axis, none: no ticks, number: tick interval,  
list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists
("text",pos) for spec of position and text. ytics_secondary ytics_secondary :

[Maxima Draw] xtics_axis (=false): x-Achsmarken am Rand, true: an der Achse [Maxima Draw] xtics_axis (=false): ticks on the boundary, true: ticks on the axis xtics_axis xtics_axis :

[Maxima Draw] ytics_axis (=false): y-Achsmarken am Rand, true: an der Achse [Maxima Draw] ytics_axis (=false): ticks on the boundary, true: ticks on the axis ytics_axis ytics_axis :

[Maxima Draw] ztics_axis (=false): z-Achsmarken am Rand, true: an der Achse [Maxima Draw] ztics_axis (=false): ticks on the boundary, true: ticks on the axis ztics_axis ztics_axis :

[Maxima Draw] xtics_secondary_axis (=false): Marken an der sekundaren (oberen) x-Achse am Rand, true: an der Achse [Maxima Draw] xtics_secondary_axis (=false): ticks on the secondary (top) boundary, true: ticks on the axis xtics_secondary_axis xtics_secondary_axis :

[Maxima Draw] ytics_secondary_axis (=false): Marken an der sekundaren (rechten) y-Achse am Rand, true: an der Achse [Maxima Draw] ytics_secondary_axis (=false): ticks on the secondary (right) boundary, true: ticks on the axis ytics_secondary_axis ytics_secondary_axis :

[Maxima Draw] xtics_rotate (=false): x-Achsmarken nicht drehen, true: um 90° drehen [Maxima Draw] xtics_rotate (=false): horizontal tick labels, true: vertical tick labels xtics_rotate xtics_rotate :

[Maxima Draw] ytics_rotate (=false): y-Achsmarken nicht drehen, true: um 90° drehen [Maxima Draw] ytics_rotate (=false): horizontal tick labels, true: vertical tick labels ytics_rotate ytics_rotate :

[Maxima Draw] ztics_rotate (=false): z-Achsmarken nicht drehen, true: um 90° drehen [Maxima Draw] ztics_rotate (=false): horizontal tick labels, true: vertical tick labels ztics_rotate ztics_rotate :

[Maxima Draw] xtics_rotate_secondary (=false): Marken an der sekundären (oberen) x-Achse nicht drehen, true: um 90° drehen [Maxima Draw] xtics_rotate_secondary (=false): don't rotate ticks of the secondary (top) x-axis, true: rotate about 90° xtics_rotate_secondary xtics_rotate_secondary :

[Maxima Draw] ytics_rotate_secondary (=false): Marken an der sekundären (rechten) y-Achse nicht drehen, true: um 90° drehen [Maxima Draw] ytics_rotate_secondary (=false): don't rotate ticks of the secondary (right) y-axis, true: rotate about 90° ytics_rotate_secondary ytics_rotate_secondary :

[Maxima Draw] xu_grid (=30) Abtastpunkte in x- oder u-Richtung [Maxima Draw] xu_grid (=30) sampling points in x- or u-direction xu_grid xu_grid :

[Maxima Draw] yv_grid (=30) Abtastpunkte in y- oder v-Richtung [Maxima Draw] yv_grid (=30) sampling points in y- or v-direction yv_grid yv_grid :

[Maxima Draw]  xyplane (=false):  xy-Koordinatenebene automatisch anordnen, Zahl: z-Koordinate [Maxima Draw3D]  xyplane (=false):  automatic allocation of the xy-plane, reak number: xy-plane intersects the z-axis at this level xyplane xyplane :

Objekte

[Maxima Draw2D] bars(b1,b2...) Säulendiagramm, Säulen gegeben durch Listen (x,h,w). Optionen: key, color, fill_color, fill_density and line_[Maxima Draw2D] bars(b1,b2...) vertical bars, given as lists (x,h,w). Options: key, color, fill_color, fill_density and line_width_bars_bars :

[Maxima Draw3D] elevation_grid(Matrix,x0,y0,w,h) Stellt eine Matrix in 3D dar. M_11 bei x=x0,y=y0+h,
M_mn bei x=x0+w,y=y0. Optionem:  xu_grid, yv_grid, line_type, key, wired_surface, enhanced3d and color [Maxima Draw3D] elevation_grid(Matrix,x0,y0,w,h) Draws a m x n-matrix in 3D. M_11 at x=x0,y=y0+h,
M_mn at x=x0+w,y=y0. Options:  xu_grid, yv_grid, line_type, key, wired_surface, enhanced3d and color_1_2_3_4_5 elevation_grid_1_2_3_4_5 elevation_grid :

[Maxima Draw2D] ellipse(xc,yc,a,b,φ1,φ2) Ellipse, zentriert bei xc, yc mit den Halbachsen a und b, von Winkel φ1 bis 
Winkel φ2. Optionen nticks, transparent, fill_color, border, line_width, line_type, key and color. [Maxima Draw2D] ellipse(xc,yc,a,b,φ1,φ2) plots an ellipse centered at [xc, yc] with horizontal and vertical semi axis a and b, respectively, 
starting at angle ang1 with an amplitude equal to angle ang2. Options: nticks, transparent, fill_color, border, line_width, line_type, key and color. #1 #2 #3 #4 #5 #6 ellipse #1 #2 #3 #4 #5 #6 ellipse :

[Maxima Draw2D] errors(e1,e2...) Punkte mit Fehlerbalken, horizontal, vertical oder beide, abhängig von der Option error_type. 
Argumente für error_type = x: Listen [x, y, xdelta] oder [x, y, xlow, xhigh]. Argumente für error_type = y; Listen [x, y, ydelta] oder [x, y, ylow, yhigh].
 Argumente für error_type = xy oder error_type = boxes: Listen [x, y, xdelta, ydelta] oder [x, y, xlow, xhigh, ylow, yhigh].  
Optionen: error_type, points_joined, line_width, key, line_type, color, fill_density, xaxis_secondary, and yaxis_secondary [Maxima Draw2D] errors(e1,e2...) Draws points with error bars, horizontally, vertically or both, depending on the value of option error_type. 
If error_type = x, arguments are lists [x, y, xdelta] or [x, y, xlow, xhigh]. If error_type = y, arguments are lists [x, y, ydelta] or [x, y, ylow, yhigh].
 If error_type = xy or error_type = boxes, arguments are lists [x, y, xdelta, ydelta] or [x, y, xlow, xhigh, ylow, yhigh].  
Options: error_type, points_joined, line_width, key, line_type, color, fill_density, xaxis_secondary, and yaxis_secondary_errors_errors :

[Maxima Draw2D] explicit(f,x,xmin,xmax) zeichnet eine Funktion f von x von xmin bis xmax. 
Optionen: nticks, adapt_depth, draw_realpart, line_width, line_type, key, filled_func, fill_color und color [Maxima Draw2D] explicit(f,x,xmin,xmax) plots explicit function f, with variable x taking values from xmin to xmax. 
Options: nticks, adapt_depth, draw_realpart, line_width, line_type, key, filled_func, fill_color and color_1_2_3_4 explicit_1_2_3_4 explicit :

[Maxima Draw3D] explicit(f,x,xmin,xmax,y,ymin,ymax) zeichnet eine Funktion f von x und y im Bereich xmin bis xmax und ymin bis ymax 
Optionen: draw_realpart, xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d und color. [Maxima Draw3D] explicit(f,x,xmin,xmax,y,ymin,ymax) plots the explicit function f, with variable x taking values from xmin to xmax and variable y 
taking values from yminto ymax. Options: draw_realpart, xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d, and color. #1 #2 #3 #4 #5 #6 #7 explicit #1 #2 #3 #4 #5 #6 #7 explicit :

[Maxima Draw2D] image(Matrix,x0,y0,w,h)  Farbdarstellung einer m x n Matrix entsprechend der Option palette [Maxima Draw2D] image(matrix,x0,y0,w,h)  plots matrix in the rectangular region from vertex (x0,y0) to (x0+w,y0+h) according
to option palette. #1 #2 #3 #4 #5 image #1 #2 #3 #4 #5 image :

[Maxima Draw2D] implicit(f,x,xmin,xmax,y,ymin,ymax)  2D Darstellung einer implizit gegebenen Funktion im angegebenen
Variablenbereich  (marching squares Algorithmus). Optionen: ip_grid, ip_grid_in, line_width, 
line_type, key, color [Maxima Draw2D] implicit(f,x,xmin,xmax,y,ymin,ymax) plots the implicit function defined by f, 
with variable x taking values from xmin to xmax, and variable y taking values from ymin to ymax. Options: ip_grid, ip_grid_in, line_width, 
line_type, key, color #1 #2 #3 #4 #5 #6 #7 implicit #1 #2 #3 #4 #5 #6 #7 implicit :

[Maxima Draw3D] implicit(f,x,xmin,xmax,y,ymin,ymax,z,zmin,zmax)  3D Darstellung einer implizit gegebenen Funktion im
 angegebenen Variablenbereich (Marching Cubes Algorithmus). Optionen: x_voxel, y_voxel, z_voxel,  
ip_grid_in, line_width, line_type, wired_surface, enhanced3D, color [Maxima Draw] [Maxima Draw3D] implicit(f,x,xmin,xmax,y,ymin,ymax,z,zmin,zmax) plots the implicit surface defined by f,
 with variable x taking values from xmin to xmax, variable y taking values from ymin to ymax and variable z taking values from zmin to zmax. 
This object implements the marching cubes algorithm. Options: x_voxel, y_voxel, z_voxel, line_width, line_type, key, wired_surface, enhanced3d,and color #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 implicit #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 implicit :

[Maxima Draw2D and 3D] label(list) Beschriftung, im 2D gegeben als Liste (text,x,y), im 3D als Liste (text,x,y,z),
spezielle Optionen: color, label_alignment, label_orientation [Maxima Draw2D and 3D] label(list) text label  specified in 2D as list [text,x,y], in 3D as list [text,x,y,z],
Options: color, label_alignment, label_orientation_label_label :

[Maxima Draw2D] parametric(fx,fy,p,pmin,pmax) parametrisch gegebenen Funktion. Optionen: 
nticks, line_width, line_type, key, color, enhanced3d [Maxima Draw2D] parametric(fx,fy,p,pmin,pmax) plots the parametric function fx, fy  with parameter p taking values from pmin to pmax. Options 
nticks, line_width, line_type, key, color, enhanced3d #1 #2 #3 #4 #5 parametric #1 #2 #3 #4 #5 parametric :

[Maxima Draw3D] parametric(fx,fy,fz,p,pmin,pmax) parametrisch gegebene Kurve. Optionen: 
nticks, line_width, line_type, key, color, enhanced3d #1 #2 #3 #4 #5 #6 parametric #1 #2 #3 #4 #5 #6 parametric :

points(matrix) Punkte, zeilenweise gegeben als n x 2 (2D) oder  n x 3 (3D)-Matrix.
Spezielle Optionen: points_joined, point_type, point_size [Maxima Draw2D/3D] [Maxima Draw2D und 3D] points(matrix) 2D: n x 2, 3D: n x 3, plots points, given as the rows in a matrix.
special options: points_joined, point_type, point_size #1 points #1 points :

points(vx,vy) Punkte, gegeben durch Vektoren der x- und y-Koordinaten.
 Spezielle Optionen: points_joined, point_type, point_size [Maxima Draw2D] [Maxima Draw2D] points(vx,vy) points given by two vectors, special options: points_joined, 
point_type, point_size #1 #2 points #1 #2 points :

[Maxima Draw3D] points(vx,vy,vz) zeichnet Punkte, gegeben durch drei Vektoren, spezielle Optionen: points_joined, 
point_type, point_size [Maxima Draw3D] points(vx,vy,vz) points given by three vectors, special options: points_joined, 
point_type, point_size #1 #2 #3 points #1 #2 #3 points :

polar() funktioniert nicht.

[Maxima Draw2D] polygon(matrix)  Polygon durch die als n x 2 Matrix gegebenen Punkte.
Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type color [Maxima Draw2D] polygon(matrix)  polygon defined by matrix (each row one point).
Special options: transparent, fill_color, border, line_width, key, line_type color #1 polygon #1 polygon :

[Maxima Draw2D]  polygon(vx,vy)  Zeichnet ein Polygon durch die als x- und y-Vektoren gegebenen Punkte.
Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type color [Maxima Draw2D]  polygon(vx,vy)  polygon defined by two vectors. Special options:
 transparent, fill_color, border, line_width, key, line_type color #1 #2 polygon #1 #2 polygon :

[Maxima Draw2D/3D] quadrilateral(l1,l2,l3,l4)  Viereck, gegeben durch Listen der Eckkoordinaten 2D: (x,y) oder 
3D: (x,y,z). Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type, color, 
enhanced3D (nur 3D) [Maxima Draw2D/3D] quadrilateral(l1,l2,l3,l4)  quadrilateral given by lists  of vertex coordinates: [x,y] in 2D or [x,y,z] in 3D.
Special options: transparent, fill_color, border, line_width, key, line_type, color, enhanced3D (3D only) #1 #2 #3 #4 quadrilateral #1 #2 #3 #4 quadrilateral :

[Maxima Draw2D]  rectangle(l1,l2)  Rechteck gegeben durch Koordinatenlisten (x,y) gegenüberliegender Ecken.
Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type, color [Maxima Draw2D]  rectangle(l1,l2)  specified by lists (x,y) of opposite corners.
Special options: transparent, fill_color, border, line_width, key, line_type, color #1 #2 rectangle #1 #2 rectangle :

[Maxima Draw2D] region(expr,x,xmin,xmax,y,ymin,ymax) Füllt das Gebiet wo expr wahr (true) ist im
Bereich von xmin, xmax, ymin, ymax. Optionen: fill_color, key, x_voxel, y_voxel [Maxima Draw2D] region(expr,x,xmin,xmax,y,ymin,ymax) Fills the region where expr is true in the
domain given by xmin, xmax, ymin, ymax. Options: fill_color, key, x_voxel, y_voxel #1 #2 #3 #4 #5 #6 #7 region #1 #2 #3 #4 #5 #6 #7 region :

spherical() funktioniert nicht

[Maxima Draw2D/3D] triangle(l1,l2,l3)  Dreieck, gegeben durch Koordinatenlisten (x,y) (2D) oder (x,y,z) (3D) der Ecken.
Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type, color [Maxima Draw2D/3D] triangle(l1,l2,l3)  given by co-ordinate lists (x,y) (2D) or (x,y,z) (3D) of the corners
Special options: transparent, fill_color, border, line_width, key, line_type, color #1 #2 #3 triangle #1 #2 #3 triangle :

[Maxima Draw3D]  tube(fx,fy,fz,fr,p,pmin,pmax)  Röhre, gegeben durch Mittellinie mit fx,fy,fz und den Radius fr
als Funktionen des Parameters p.
Spezielle Optionen:  xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d, 
color,tube_extremes. [Maxima Draw3D]  tube(fx,fy,fz,fr,p,pmin,pmax)  tube, given by functions fx,fy,fz of the centerline and radius function fr
pf parameters p.
Special options:  xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d, 
color,tube_extremes. #1 #2 #3 #4 #5 #6 #7 tube #1 #2 #3 #4 #5 #6 #7 tube :

[Maxima Draw2D/3D]  vector(l1,l2)  Pfeil,  gegeben durch Koordinatenlisten (x,y) (2D) oder (x,y,z) (3D) der Endpunkte.
Spezielle Optionen:  head_both, head_length, head_angle, head_type, line_width, line_type, key 
color. [Maxima Draw2D/3D]  vector(l1,l2)  given by co-ordinate lists (x,y) (2D) or (x,y,z) (3D) of the end points.
Spezielle Optionen:  head_both, head_length, head_angle, head_type, line_width, line_type, key 
color. #1 #2 vector #1 #2 vector :

[Maxima]  set(e1, e2,...) Maxima set (Liste in geschweiften Klammern) [Maxima]  set(e1, e2,...) Maxima set (in Maxima this is a list in curly braces)_set_set :

[Maxima] args(expr) Liste der Argumente von expr [Maxima] args(expr) list of the top level arguments of expr_args_args :

Sonstige

[Maxima] true true :

[Maxima] false false :

f.x u - 2 ρ * b u * cosh * b u * sinh * u v d / + :

f.y 2 w * b u * cosh * w v cos * w v * cos * - v sin w v * sin * - (* u v d / :

f.z 2 w * b u * cosh * w v sin * w v * cos * - v cos w v * sin * - (* u v d / :

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terminal=pngcairo file_name="C:/Users/kraska/AppData/Roaming/SMath/extensions/plugins/44011c1e-5d0d-4533-8e68-e32b5badce41/GnuPlot/15uoh1wa" dimensions=[391;299] font="Arial" font_size=8 xu_grid=40 yv_grid=40 xlabel="x" ylabel="y" zlabel="z" xrange=[-7.2;7.2] yrange=[-7.2;7.2] zrange=[-7.2;7.2] "set term pngcairo font ',8' enhanced size 391, 299" "set encoding iso_8859_2" "set view 10, 329, 1, 1" plot3D SAMPLE PLOT Sample Disable Disable 4095 8 Disable Arial Disable 5 Disable [blue,red,green] 40 40 Custom 391 299 Interactive C:/Users/kraska/AppData/Roaming/SMath/extensions/plugins/44011c1e-5d0d-4533-8e68-e32b5badce41/GnuPlot/15uoh1wa png Disable x y z Default Default Default -7.2 7.2 -7.2 7.2 -7.2 7.2 Interactive Interactive Interactive Disable Disable Disable Disable Disable Disable 10 10 10 329 10 1 1 Interactive Disable MouseX1 MouseY1 MouseW1 Disable Azimuth1 Zenith1 Disable MinX1 MaxX1 Disable MinY1 MaxY1 Disable MinZ1 MaxZ1 proportional_axes xyz ≡ axis_3d false ≡ surface_hide true ≡ xtics none ≡ ytics none ≡ ztics none ≡ xu_grid 50 ≡ yv_grid 50 ≡ f.x f.y f.z u 12 - 12 v 4 - 4 parametric_surface 9 1 sys

par

If you want a nice view of fixed rotation <= disable ... enable =>

γ 0.7857 0.6177 0.0337 0.2065 0.3132 - 0.927 0.5831 0.7214 - 0.3736 - 33 mat

γ 0.5 0.5128 0.0131 - 0.5128 - 0.5 0.0128 0.0131 0.0128 133 mat :

zoom 0.875 :

M t f t B M zoom * γ * eval : t B 1 col t B 2 col augment 21 line :

step1 00 range :

c 00 + 200 red 15 mat :

Figure 44 - Breather 14 black 15 mat :

Quaternion rotation

M t f c Figure 3 1 sys

The 3D solid Breather will produce few Quaternion rotation that will not hurt the eyes. The combined Quaternion is very reactive and Breather explodes easily ... α= 0.5, β= 1, p= 0.2 are acceptable. Euler rotation of Breather is more manageable.

Some nice Breather from Mathcad 11 Quaternion, meshed 199 x 199 Would be great if Smath could render something like GNU plot Kuen surface example. As it looks from work sheet above, Smath does not access Maxima 3D plot ?