geom3d - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Sphere Functions : geom3d/FindAngle

geom3d

  

FindAngle

  

find the angle between two given objects

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

FindAngle(l1, l2)

FindAngle(p1, p2)

FindAngle(s1, s2)

FindAngle(l1, p1)

FindAngle(A, T)

Parameters

l1, l2

-

lines

p1, p2

-

planes

s1, s2

-

sphere

A

-

a point

T

-

a triangle

Description

• 

When two lines l1, l2 do not intersect, we define the angle determined by them as the angle between two lines through the origin parallel to the given lines. It is the convention that the angle returned is in the interval [0,Pi/2].

• 

The angle between two planes p1, p2 is equal to the angle between their normals.

• 

The angle of intersection of two spheres s1 and s2 at a common point is the angle between the tangent-planes to the spheres at that points. Note that at all common points, the angle of intersection is the same.

• 

The angle between a straight line l1 and a plane p1 is equal to the complement of the angle between the straight line and the normal of the plane.

• 

If T is a triangle, and A a vertex of T, FindAngle(A,T) returns the internal angle of T at A.

• 

The command with(geom3d,FindAngle) allows the use of the abbreviated form of this command.

Examples

withgeom3d:

Find the angle between a line and a plane

make necessary assumptions

assumel0,lp0:

planep1,lx+my+nz+p=0,x,y,z:

linel1,pointA,x1,y1,z1,lp,mp,np:

FindAnglel1,p1

arcsinlp~l~+mmp+nnpl~2+m2+n2lp~2+mp2+np2

(1)

l'l':lp'lp':

If the point P(a,b,c) perpendiculars PM, PN are drawn to the planes of zx, xy, find the equation of the plane OMN and the angle which OP makes with it.

assumea0,b0,c0

pointP,a,b,c:

pointo,0,0,0,pointX,1,0,0,pointY,0,1,0,pointZ,0,0,1:

planeoxz,o,X,Z,planeoxy,o,X,Y:

projectionM,P,oxz:projectionN,P,oxy:

planep,o,M,N

p

(2)

Equationp,x,y,z

a~b~z+a~c~yb~c~x=0

(3)

lineOP,o,P:

FindAngleOP,p

arcsinb~c~a~a~2b~2+a~2c~2+b~2c~2a~2+b~2+c~2

(4)

See Also

geom3d[distance]

geom3d[line]

geom3d[plane]

geom3d[sphere]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam