- POV-Ray Tutorials
- Analytical Geometry
with POV-Ray
- Index -
- Insert Menu Add-on
& Download
- Basics
Possibilities and Needs
Points & Lines
- Points in 3D
- Line Sections, Straight,
Vectors, Distance Markers
- Surfaces & Planes
- Output of Results,
Captions
- Points of Intersection
- Circles
Solids
- Tetrahedron
- Parallelepiped
- Round Solids
-
- Overview by Table
on "analytical_g.inc"
- Vector Analysis
with POV-Ray
- Righthanded & Lefthanded
Systems of Coordinates
and the Cross Product
- Samples from
Analytical Geometry
- Parallelogram of the
Middles of the Edges
- Trace Points of a Straight Line
- Calculations
about a Triangle
- Area of a Parallelogram
and Cross Product
- Shadow of a Pyramid
- Hit a plane || yz-plane
> Angle triange yz-plane
|
Analytical Geometry with POV-Ray
- Samples - |
|
|
Angle between a triange
and the yz-plane. |
|
The triangle is given by 3 points:
(For details on textures see the scene file!)
#declare A = <-0.00,1.20,-1.00>;
// and 2 point s on a plane || to yz:
#declare B = < 2.00,1.50, 1.50>;
#declare C = < 2.00,0.00,-1.000>;
// Showing points A, B and C:
sphere{ <0,0,0>, 0.075 translate A
texture{ T_YellowGreen }
}
sphere{ <0,0,0>, 0.075 translate B
texture{ T_Yellow }
}
sphere{ <0,0,0>, 0.075 translate C
texture{ T_Orange }
}
triangle{ A,B,C
pigment{color rgbt<1,1,0.5,0.5>}}
// and the plane x = 2:
box { <0.00, 0.00,-2.00>,< 0.025, 5.00, 3.50>
texture { pigment{ color rgb<1, 1, 1>}
finish { phong 1 }
} // end of texture
translate C
} // end of box --------------------------
Calculation of the base point P of a line
perpendicular to the line CB:
// Angle between AC and BC at point C:
#declare Angle_C = degrees(VAngle(B-C,A-C));
// Distance from C to the base point P
// of a line perpendicular to BC:
#declare Len_P = vlength(A-C)*cos(radians(Angle_C));
// Base point P on line CB:
#declare P = C + (B-C)*Len_P/vlength(B-C);
// Show P (red)
sphere{ <0,0,0>, 0.08 translate P
texture{ T_Red }
} |
Base Point P of a line
perpendicular to the line CB
|
|
Calculation of the angle between the triangle ABC
and a plane parallel to the yz-plane:
#declare PA_Vector = A-P ;
object{ Vector( <0,0,0>,PA_Vector, 0.025)
translate P
texture{ T_Lila }
}
// vertical to CL on plane x=2:
#declare PB_Vector = B-P;
object{ Vector( <0,0,0>,PB_Vector, 0.025)
translate P
texture{ T_Cyan }
}
Vertical to PB in plane x=2:
[ The components of a vector: A=<A.x,A.y,A.z>]
Note:
A 2D-vector V1 = < x1, y1> is perpendicular
to a vector V2 = <-y1, x1> !
By analogy:
A 3D-vector V1 = < 0, y1, z1> is perpendicular
to a vector V2 = < 0, -z1, y1> !
#declare Vertical_to_PB =
<0,PB_Vector.z,-PB_Vector.y> ;
object{ Vector(<0,0,0>,Vertical_to_PB, 0.025)
translate P
pigment{ rgb<1,0,0.5> }
}
// Angle between vector PA (violet) and
// vector perpenticular to PB in plane x=2
// (wine red)
#declare Angle_ABC_to_Plane =
degrees(VAngle(Vertical_to_PB,PA_Vector));
// Angle between CB and z direction:
#declare Angle_PB_to_Z =
degrees(atan((B.y-C.y)/(B.z-C.z)));
|
Angle between a triangle and
a plane parallel to the yz-plane.
This scene for POV-Ray:
"AngleTriangle2Plane_1.pov" file
Needs my include file: "shapes_lo.inc" (see 'step 2')
Note: If we have a triange with only one point on the plane || to the yz plane, we
need to calculate the second point on the plane like in 'Hit a plane || yz-plane'.
Animation see here!
|
|
