1. Krivky. krivky zadane parametrickymi rovnicemi. Primka rovnobezna s osou y. Primka rovnobezna s osou x

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1 1. Krivky krivky zadane parametrickymi rovnicemi krivka K: x = f(t), y = g(t), t 2interval <a,b obrazek dostanu pomoci: plot([f(t),g(t),t = a..b]) Primka rovnobezna s osou y plot([1, y, y = ], thickness = 3, linestyle = dash); Primka rovnobezna s osou x plot([x, 1, x = ], thickness = 3, linestyle = dashdot);

2 Elipsa plot([3*cos(t), sin(t), t = 0.. 2*Pi], scaling = constrained);

3 Asymptoty plot([[x, 1/(x-1), x = ], [1, y, y = ]], discont = true, linestyle = [solid, dash]);

4 a := plot([x, 1/(x-1), x = ], discont = true, linestyle = solid, view = [-4.. 4, ]): b := plot([1, y, y = ], discont = true, linestyle = dash, color = grey): plots[display](a, b);

5 krivky popsane rovnici krivka K: F(x,y)=0 obrazek dostanu pomoci prikazu z balicku plots: implicitplot( F(x,y) = 0, x = min.. max, y = min.. max ) a := plots[implicitplot](x = 1, x = , y = , linestyle = dash, color = grey); b := plot(1/(x-1), x = , discont = true); plots[display](a, b, view = [-2.. 3, ]); (1.2.1) (1.2.2)

6 plots[implicitplot](x^2+4*(y+1)^2 = 1, x = , y = , scaling = constrained, numpoints = 5000);

7 obrazek v souradnem systemu, kde meritka na jednotlivych osach jsou stejne, t.j. v pomeru 1:1 (scaling = constrained) aby se obrazek "vyhladil" - vice bodu, ve kterych Maple vyhodnocuje predpis krivky (numpoints = 5000 (napriklad)) 2. Uzitecne poznamky kresleni geometrickych utvaru Bod: plot([[1, 2]], style = point, symbol = diamond, symbolsize = 20);

8 Mnozina bodu: plot([[1, 2], [1, 3], [2, 0]], style = point, symbol = solidcircle, symbolsize = 20);

9 Body lezici na grafu funkce: plot(x^2, x = 0.. 2, style = point, symbolsize = 30, numpoints = 5, adaptive = false);

10 Usecka: plot([[1, 1], [2, 3]], thickness = 3, view = [0.. 3, 0.. 4]);

11 Jiny zpusob - pouziti balicku plottools with(plottools); with(plots); (2.1.1) display(line([1, 1], [2, 3]), view = [0.. 3, 0.. 4]);

12 display(point([1, 1], symbol = cross, symbolsize = 25));

13 display(curve([[1, 2], [2, 0], [3, 1], [4, 2], [0, 0]]));

14 titulek s matematickym vyrazem plot(exp(x), x = , title = typeset("graf funkce ", exp(x), " na intervalu ", [-5, 0]), titlefont = ["Helvetica", 16]);

15 plot(exp(x), x = , title = typeset("graf funkce ", exp(x), " na intervalu ", [-5, 0]), titlefont = ["Helvetica", 16]);

16 plot(exp(x), x = , title = typeset("graf funkce ", exp(x), " na intervalu ", [-5, 0]), titlefont = ["Helvetica", 16]);

17 plot(exp(x), x = , title = typeset("graf funkce ", exp(x), " na intervalu ", [-5, 0]), titlefont = ["Helvetica", 16]);

18 gridlines plot([[1.4, 3], [2.5, 4], [.7, 1.9]], style = point, symbol = solidcircle, symbolsize = 20, view = [0.. 3, 0.. 5], gridlines = true);

19 plot([[1.4, 3.6], [2.5, 2.3], [.7, 1.9]], style = point, symbol = solidcircle, symbolsize = 20, view = [0.. 3, 0.. 5], axis = [gridlines = [color = "grey", linestyle = dash]], tickmarks = [[.7, 1.4, 2.5], default]);

20 plot([[1.4, 3.6], [2.5, 2.3], [.7, 1.9]], style = point, symbol = solidcircle, symbolsize = 20, view = [0.. 3, 0.. 5], axis = [gridlines = [color = "grey", linestyle = dash]], tickmarks = [[.7, 1.4, 2.5], [3.6, 2.3, 1.9]]);

21 plot([[1.4, 3.6], [2.5, 2.3], [.7, 1.9]], style = point, symbol = solidcircle, symbolsize = 20, view = [0.. 3, 0.. 5], axis[1] = [gridlines = [color = "grey", linestyle = dash]], tickmarks = [[.7, 1.4, 2.5], [3.6, 2.3, 1.9]]);

22 3. Grafy funkci dvou promennych plot3d - options - color, style, tickmarks, title, view... - transparency = 0 default (0 - netransparentni, 1 - transparentni) - grid = [25,25] default - y = f(x).. g(x) - definicni obor nemusi byt jenom kartezsky soucin intervalu plot3d(x^2+y^2, x = , y = , axes = boxed, grid = [20, 10]);

23 plot3d(x^2+y^2, x = 0.. 2, y = *x, transparency = 1/3, axes = normal, axis[1] = [color = blue], axis[2] = [color = red], style = polygonoutline);

24 vic grafu v jednom obrazku pouzitim seznamu plot3d([sin(x+y), cos(x+y)], x = , y = , color = [red, blue], axes = boxed, lightmodel = light1, style = surface);

25 Poznamka: A list of three algebraic expressions or procedures is always interpreted as a parametric plot. To specify a list of three distinct plots, the option plotlist=true (or simply plotlist) must be provided. plot3d([x, y, x+y], x = , y = , axes = framed);

26 plot3d([x, y, x+y], x = , y = , axes = framed, plotlist = true);

27 pouzitim prikazu display a := plot3d(x^2+y^2, x = , y = , transparency = 1/2, axes = framed, color = blue); ( ) b := plot3d(-x^2-y^2+20, x = , y = , transparency = 1/2, axes = framed, color = red); ( ) plots[display](a, b, view = [-5.. 5, , ]) ;

28 vrstevnice plots[contourplot](sin(x)*sin(y), x = -Pi.. Pi, y = -Pi.. Pi);

29 plots[contourplot](sin(x)*sin(y), x = -Pi.. Pi, y = -Pi.. Pi, contours = [-1/2, 1/4, 1/2]);

30 plots[contourplot](sin(x)*sin(y), x = -Pi.. Pi, y = -Pi.. Pi, contours = 20);

31 nastavenim hodnoty parametru style v prikazu plot3d plot3d(sin(x)*sin(y), x = -Pi.. Pi, y = -Pi.. Pi, style = surfacecontour, contours = [-2/3, -1/2, 0, 1/2, 2/3]);

32 plot3d(sin(x)*sin(y), x = -Pi.. Pi, y = -Pi.. Pi, style = contour, filledregion = true, linestyle = solid, color = black);

33 prikazem contourplot3d z balicku plots plots[contourplot3d](sin(x)*sin(y), x = -Pi.. Pi, y = -Pi.. Pi, contours = 20, filledregion = true, coloring = [violet, black], transparency = 2/3);

34 a jejich prumetu do roviny z = konst (vrstevnice pro z = 0) do jedneho obrazku with(plottools); ( ) with(plots); ( )

35 p := plot3d(1/(x^2+y^2+1), x = , y = , style = contour, contours = 8, filledregion = true, color = pink); [Length of output exceeds limit of ] ( ) q := contourplot(1/(x^2+y^2+1), x = , y = ); ( ) f:=transform((x,y)-[x, y, 0]): display({p, f(q)}, axes = boxed); 4. Plochy plochy zadane parametrickymi rovnicemi plocha: x = f (t,s)

36 h(t,s)], t = a..b, s = c..d) z = h (t,s), t 2 <a,b, s 2 <c,d plochy popsane rovnici plocha: [implicitplot3d]( F(x,y,z) = 0, x = min..max, y = min..max, z = min..max ) plots[implicitplot3d](x^2+y^2+z^2 = 10, x = , y = , z = , axes = frame, style = surface, grid = [50, 50, 50]);

37 vic ploch v jednom obrazku pomoci prikazu display a := plots[implicitplot3d](x^2+y^2+z^2 = 2, x = , y = , z = , style = surfacecontour, color = black, grid = [50, 50, 50], transparency =.5); [Length of output exceeds limit of ] ( ) b := plot3d([sin(t)*cos(s), cos(t)*sin(s), cos(t)], t = 0.. 2*Pi, s = 0.. 2*Pi, transparency =.5); plots[display](b, a, axes = boxed); ( )

38 pomoci seznamu plots[implicitplot3d]([x = 1/2, y = 1, z = 1.5], x = 0.. 2, y = 0.. 2, z = 0.. 2, axes = boxed, color = [pink, violet, grey]);

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