quiver3

3-D quiver or vector plot

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Syntax

quiver3(X,Y,Z,U,V,W)

quiver3(Z,U,V,W)

quiver3(___,scale)

quiver3(___,LineSpec)

quiver3(___,LineSpec,'filled')

quiver3(___,Name,Value)

quiver3(ax,___)

q = quiver3(___)

Description

example

quiver3(X,Y,Z,U,V,W) plots arrows with directional components U, V, and W at the Cartesian coordinates specified by X, Y, and Z. For example, the first arrow originates from the point X(1), Y(1), and Z(1), extends in the direction of the x-axis according to U(1), extends in the direction of the y-axis according to V(1), and extends in the direction of the z-axis according to W(1). By default, the quiver3 function scales the arrow lengths so that they do not overlap.

quiver3(Z,U,V,W) plots arrows with directional components specified by U, V, and W at equally spaced points along the surface Z.

If Z is a vector, then the x-coordinates of the arrows range from 1 to the number of elements in Z and the y-coordinates are all 1.
If Z is a matrix, then the x-coordinates of the arrows range from 1 to the number of columns in Z and the y-coordinates range from 1 to the number of rows in Z.

example

quiver3(___,scale) adjusts the length of arrows:

When scale is a positive number, the quiver3 function automatically adjusts the lengths of arrows so they do not overlap, then stretches them by a factor of scale. For example, a scale of 2 doubles the length of arrows, and a scale of 0.5 halves the length of arrows.
When scale is 'off' or 0, such as quiver3(X,Y,Z,U,V,W,'off'), then automatic scaling is disabled.

example

quiver3(___,LineSpec) sets the line style, marker, and color. Markers appear at the points specified by X, Y, and Z. If you specify a marker using LineSpec, then quiver3 does not display arrowheads. To specify a marker and display arrowheads, set the Marker property instead.

quiver3(___,LineSpec,'filled') fills the markers specified by LineSpec.

quiver3(___,Name,Value) specifies quiver properties using one or more name-value pair arguments. For a list of properties, see Quiver Properties. Specify name-value pair arguments after all other input arguments. Name-value pair arguments apply to all of the arrows in the quiver plot.

example

quiver3(ax,___) creates the quiver plot in the axes specified by ax instead of the current axes (gca). The argument ax can precede any of the input argument combinations in the previous syntaxes.

example

q = quiver3(___) returns a Quiver object. This object is useful for controlling the properties of the quiver plot after creating it.

Examples

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Create 3-D Quiver Plot

Open Live Script

Load sample data that represents air currents over North America. For this example, select a subset of the data.

load wind
X = x(5:10,20:25,6:10);
Y = y(5:10,20:25,6:10);
Z = z(5:10,20:25,6:10);
U = u(5:10,20:25,6:10);
V = v(5:10,20:25,6:10);
W = w(5:10,20:25,6:10);

Create a 3-D quiver plot of the subset you selected. The vectors X, Y, and Z represent the location of the base of each arrow, and U, V, and W represent the directional components of each arrow. By default, the quiver3 function shortens the arrows so they do not overlap. Call axis equal to use equal data unit lengths along each axis. This makes the arrows point in the correct direction.

quiver3(X,Y,Z,U,V,W)
axis equal

Figure contains an axes. The axes contains an object of type quiver.

Disable Automatic Scaling

Open Live Script

By default, the quiver3 function shortens arrows so they do not overlap. To disable automatic scaling so that arrow lengths are determined entirely by U, V, and W, set the scale argument to 0.

For example, first return the x-, y-, and z-coordinates of a unit sphere with 10-by-10 faces. Calculate the directional components of its surface normals using the surfnorm function. Then, create a 3-D quiver plot with no automatic scaling.

[X,Y,Z] = sphere(10);
[U,V,W] = surfnorm(X,Y,Z);
quiver3(X,Y,Z,U,V,W,0)
axis equal

Figure contains an axes. The axes contains an object of type quiver.

For comparison, create the plot with automatic scaling. Note that the arrows are shorter and do not overlap.

figure
quiver3(X,Y,Z,U,V,W)
axis equal

Figure contains an axes. The axes contains an object of type quiver.

Plot Vectors Normal to Surface

Open Live Script

Plot vectors that are normal to the surface defined by the function $z = x e^{- x^{2} - y^{2}}$ . Use the quiver3 function to plot the vectors and the surf function to plot the surface.

First, create a grid of x- and y-values that are equally spaced. Use them to calculate z. Then, find the normal vectors.

[X,Y] = meshgrid(-2:0.25:2,-1:0.2:1);
Z = X.*exp(-X.^2 - Y.^2);
[U,V,W] = surfnorm(X,Y,Z);

Display the vectors as a 3-D quiver plot. Then, display the surface in the same axes. Adjust the display so that the vectors appear normal to the surface by calling axis equal.

quiver3(X,Y,Z,U,V,W)
hold on
surf(X,Y,Z)
axis equal

Figure contains an axes. The axes contains 2 objects of type quiver, surface.

Specify Arrow Color

Open Live Script

Create a 3-D quiver plot and specify a color for the arrows.

For example, first return the x-, y-, and z- coordinates of a surface. Calculate the directional components of its surface normals using the surfnorm function.

[X,Y] = meshgrid(-pi/2:pi/8:pi/2,-pi/2:pi/8:pi/2);
Z = sin(X) + cos(Y);
[U,V,W] = surfnorm(Z);

Then, create a 3-D quiver plot with red arrows.

quiver3(X,Y,Z,U,V,W,'r')
axis equal

Figure contains an axes. The axes contains an object of type quiver.

Specify Axes for 3-D Quiver Plot

Open Live Script

Starting in R2019b, you can display a tiling of plots using the tiledlayout and nexttile functions. Call the tiledlayout function to create a 1-by-2 tiled chart layout. Call the nexttile function to create an axes object and return the object as ax1. Create the left plot by passing ax1 to the quiver3 function. Add a title to the plot by passing the axes to the title function. Repeat the process to create the right plot.

[X,Y] = meshgrid(-2:0.25:0,-2:0.25:0);
Z1 = -0.5*(X.^2 + Y.^2);
[U1,V1,W1] = surfnorm(Z1);
Z2 = -X.*Y;
[U2,V2,W2] = surfnorm(Z2);

tiledlayout(1,2)

% Left plot
ax1 = nexttile;
quiver3(ax1,X,Y,Z1,U1,V1,W1)
axis equal
title(ax1,'Left Plot')

% Right plot
ax2 = nexttile;
quiver3(ax2,X,Y,Z2,U2,V2,W2)
axis equal
title(ax2,'Right Plot')

Figure contains 2 axes. Axes 1 with title Left Plot contains an object of type quiver. Axes 2 with title Right Plot contains an object of type quiver.

Modify 3-D Quiver Plot After Creation

Open Live Script

Create a 3-D quiver plot and return the quiver object. Then, remove the arrowheads and add dot markers at the base of each arrow.

[X,Y] = meshgrid(-3:0.5:3,-3:0.5:3);
Z = 0.2*(Y.^2 - X.^2);
[U,V,W] = surfnorm(Z);

q = quiver3(X,Y,Z,U,V,W);
axis equal
q.ShowArrowHead = 'off';
q.Marker = '.';

Figure contains an axes. The axes contains an object of type quiver.

Input Arguments

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`X` — x-coordinates of bases of arrows
scalar | vector | matrix

x-coordinates of the bases of arrows, specified as a scalar, a vector, or a matrix.

If X and Y are vectors and Z, U, V, and W are matrices, then quiver3 expands X and Y into matrices. In this case, size(Z), size(U), size(V), and size(W) must equal [length(Y) length(X)]. For more information about expanding vectors into matrices, see meshgrid.