Revisions to How to generate 3D spherical sector

deleted 4 characters in body

edited Dec 19, 2016 at 12:08

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Definition of the region:

reg := ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *)   θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *)   φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *)  );

Definition of the parameters:

{r1, r2, θ1, θ2, φ1, φ2} = {2, 2.2, 30°, 180°, 15°, 85°};

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}],    PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°]

RegionPlot3D[reg, {x, -2.5, 2.5}, {y, -2.5, 2.5}, {z, -2.5, 2.5}, Axes -> False,   PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°, Axes -> False, Mesh -> None]

Definition of the region:

reg := ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *) θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *) φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *) );

Definition of the parameters:

{r1, r2, θ1, θ2, φ1, φ2} = {2, 2.2, 30°, 180°, 15°, 85°};

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}],  PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°]

RegionPlot3D[reg, {x, -2.5, 2.5}, {y, -2.5, 2.5}, {z, -2.5, 2.5}, PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°, Axes -> False, Mesh -> None]

Definition of the region:

reg := (r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *)   θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *)   φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *)  );

Definition of the parameters:

{r1, r2, θ1, θ2, φ1, φ2} = {2, 2.2, 30°, 180°, 15°, 85°};

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}],   PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°]

RegionPlot3D[reg, {x, -2.5, 2.5}, {y, -2.5, 2.5}, {z, -2.5, 2.5}, Axes -> False,   PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°, Mesh -> None]

Changed numerical values and plots.

Source Link

edited Sep 11, 2016 at 10:26

user31159

Definition of the region:

reg := ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *) θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *) φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *) );

Definition of the parameters:

{r1 =, 3; r2 =, 4; θ1 =, 30°; θ2 =, 80°; φ1 =, 15°; φ2} = 75°;{2, 2.2, 30°, 180°, 15°, 85°};

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}], PlotPoints -> 80, Boxed -> False, ViewAngle -> 30°]20°]

RegionPlot3D[reg, {x, 0-2.5, 42.5}, {y, 0-2.5, 42.5}, {z, 0-2.5, 42.5}, PlotPoints -> 4080, Boxed -> False, ViewAngle -> 30°20°, Axes -> False, Mesh -> None]

Definition of the region:

reg := ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *) θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *) φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *) );

Definition of the parameters:

r1 = 3; r2 = 4; θ1 = 30°; θ2 = 80°; φ1 = 15°; φ2 = 75°;

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}], PlotPoints -> 80, Boxed -> False, ViewAngle -> 30°]

RegionPlot3D[reg, {x, 0, 4}, {y, 0, 4}, {z, 0, 4}, PlotPoints -> 40, Boxed -> False, ViewAngle -> 30°, Axes -> False, Mesh -> None]

Definition of the region:

reg := ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *) θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *) φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *) );

Definition of the parameters:

{r1, r2, θ1, θ2, φ1, φ2} = {2, 2.2, 30°, 180°, 15°, 85°};

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}], PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°]

RegionPlot3D[reg, {x, -2.5, 2.5}, {y, -2.5, 2.5}, {z, -2.5, 2.5}, PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°, Axes -> False, Mesh -> None]

added 1 character in body

Source Link

edited Sep 11, 2016 at 2:44

user31159

Definition of the region:

reg := ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *) θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *) φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *) );

Definition of the parameters:

r1 = 3; r2 = 4; θ1 = 30°; θ2 = 80°; φ1 = 15°; φ2 = 75°;

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}], PlotPoints -> 80, Boxed -> False, ViewAngle -> 30°]

RegionPlot3D[reg, {x, 0, 4}, {y, 0, 4}, {z, 0, 4}, PlotPoints -> 40, Boxed -> False, ViewAngle -> 30°, Axes -> False, Mesh -> None]

Definition of the region:

reg = ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *) θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *) φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *) );

Definition of the parameters:

r1 = 3; r2 = 4; θ1 = 30°; θ2 = 80°; φ1 = 15°; φ2 = 75°;

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}], PlotPoints -> 80, Boxed -> False, ViewAngle -> 30°]

RegionPlot3D[reg, {x, 0, 4}, {y, 0, 4}, {z, 0, 4}, PlotPoints -> 40, Boxed -> False, ViewAngle -> 30°, Axes -> False, Mesh -> None]

Definition of the region:

reg := ( r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *) θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *) φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *) );

Definition of the parameters:

r1 = 3; r2 = 4; θ1 = 30°; θ2 = 80°; φ1 = 15°; φ2 = 75°;

Plots:

RegionPlot3D[ImplicitRegion[reg, {x, y, z}], PlotPoints -> 80, Boxed -> False, ViewAngle -> 30°]

RegionPlot3D[reg, {x, 0, 4}, {y, 0, 4}, {z, 0, 4}, PlotPoints -> 40, Boxed -> False, ViewAngle -> 30°, Axes -> False, Mesh -> None]

Source Link

answered Sep 11, 2016 at 2:33

user31159

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