Analytical Geometry with POV-Ray
Overview by Table
about the most important commands for a quick orientation
Definition of the points:
Following vectors are predefined in POV-Ray:
o = <0,0,0>,(center of the world)
x = <1,0,0>, y = <0,1,0>, z = <0,0,1>
Define variables for our own point and vectors, i.e.:
P1 = < 2, 1.5, -3>;
V1 = < -3, 1.25, 1>;
In sample file "a_geo_00.pov" predefined is:
Rp = 0.105 = radius of the points,
Rl = 0.055 = radius of the lines
and also the basic colors here.
Representation of objects:
(Most of here used macros are defined
in my include file analytical_g.inc
Alternativly: download analytical_g.txt and save
it with the name "analytical_g.inc"
.) |
Textures of the
template scene file "a_geo_00.pov"
or
template scene file "a_geo_00.txt"
|
Punkt P1:
....................... sphere{ P1, Rp pigment{ color Red } }
Unambiguous marking of positions:
1) Wire_box-Method :
object{ Wire_Box( o, P,Rl/2,0) pigment{ color Yellow }},
2) Suporting cylinder in y direction:
object{ Show_Y_( P, Rl/2) pigment{ color Yellow } }.
3) Suporting cylinder in y direction with projections of xz components:
object{ Show_Yxz( P, Rl/2) pigment{ color Yellow } }.
Line section P1P2:
.............. cylinder{ P1, P2, Rl pigment{ color Green}}
Straight line P1P2:
................ cylinder{ P1–10*(P2-P1), P2+10*(P2-P1), Rl pigment{ color Green}}
Vector P1P2:
.................. object{ Vector (P1, P2, Rl) pigment{ color Green}}
Distance marker P1P2:
object{ Distance_Marker(P1, P2, Rl) pigment{ color Green}}
Triangle P1P2P3:
.............. triangle { P1, P2, P3 pigment{ color Yellow transmit 0.5 }
Normal vector on triangle P1P2P3:
......... object{ Triangle_Normal (P1, P2, P3) pigment{ color Yellow }
Mass center of a triangle P1P2P3:
object{ Triangle_Mass_Center (P1, P2, P3) pigment{ color Yellow }
Area of a triangle P1P2P3:
........... Triangle_Area ( P1, P2, P3 )
Circumference of a triangle P1P2P3:
......... Triangle_Circum ( P1, P2, P3 )
Plane
by Parameters:
..... object{ Plane_Dir( Start, Dir1, Dir2, Start, End ) pigment{ color Green}}
by Normal Representation, N=<A,B,C>, D:
..... object{ Plane_Nor( Normal, D, Start, End) pigment{ color Green}}
Normal Representation, with N and a point P:
... object{ Plane_NoP( Normal, P, Start, End) pigment{ color Green}}
Point of intersection of straght line and plane
Line by i.e. start point and direction #declare P = <x1,x2,x3> #declare Dir = <d1,d2,d3>
Plane declared as an object: #declare Plane = ...; s.o.
#declare Point_of_intersection = trace ( Plane, A, Dir )
With normal vector in the point of intersection - name predeclared by: #declare Normal = <0,0,0>
#declare Point_of_intersection = trace ( Plane, A, Dir, Normal)
Circle (M,r) around axis:
Circle line: ............... object{ Circle_Line ( Center, Radius, Rl, Axis) pigment{ color Yellow }}
Circle area ............. object{ Circle_Disc ( Center, Radius, Axis) pigment{ color Yellow transmit 0.5 }}
Circum circle of a triangle P1P2P3:
Circle line: ............... object{ Circle_Line_out( P1, P2, P3, Rl) pigment{ color Yellow }}
Circle area ............. object{ Circle_Disc_out( P1, P2, P3 ) pigment{ color Yellow transmit 0.5 }}
Circumcircle center. object{ Triangle_M_out( P1, P2, P3 ) pigment{ color Green }}
Circumcircle radius ......... Triangle_R_out( P1, P2, P3 )
Incircle of a triangle P1P2P3:
Circle line: ............... object{ Circle_Line_in ( P1, P2, P3, Rl) pigment{ color Yellow }}
Circle area ............. object{ Circle_Disc_in ( P1, P2, P3 ) pigment{ color Yellow transmit 0.5 }}
Incircle center .. object{ Triangle_M_in ( P1, P2, P3 ) pigment{ color Green }}
Incircle radius ........... Triangle_R_in ( P1, P2, P3 )
Tetrahedron
by edge vectors V1,V2,V3:
object{ Tetrahedron_by_Edges ( V1,V2,V3, Rl,Rp, Filled) pigment{ color Green transmit 0.5}}
by corners P1P2P3P4:
.... object{ Tetrahedron_by_Corners ( P0,P1,P2,P3, Rl,Rp, Filled) pigment{ color Green transmit 0.5}}
Parallelepiped
by edge vectors V1,V2,V3:
object{ Parallelepiped_by_Edges ( V1,V2,V3, Rl,Rp, Filled) pigment{ color Green transmit 0.5}}
by corners P1P2P3P4:
.... object{ Parallelepiped_by_Corners( P0,P1,P2,P3, Rl,Rp, Filled) pigment{ color Green transmit 0.5}}
Sphere with center M and radius R:
........... sphere { Center, R pigment{ color White }
Ellipsoid, center M, radii Rx,Ry,Rz:
.. sphere { Center, R scale pigment{ color Green transmit 0.5 }
Cylinder, centers of the ends M1 and M2
and radius R:
................................................... cylinder { M1,M1, R pigment{ color Green transmit 0.5 }
Cone with base center M1,
base radius R1 and top at M2:
......................... cone { M1,R1, M2, 0 pigment{ color Green transmit 0.5 }
Truncated cone, centers of the ends M1, M2
and radii R1 and R2:
..................................... cone { M1,R1, M2, R2 pigment{ color Green transmit 0.5 }
Text objects to add a caption + caculated values to objects:
| Caption "P": |
text { ttf "ARIAL.TTF", "P",0.1,0
scale 0.5 rotate<20,-45,0>
translate P + <-0.2,0.3,0>
pigment{ color Red } no_shadow} |
Caption "|PQ|"
+ value: |
text{ ttf "ARIAL.TTF"
concat( "|PQ| = " , str(vlength( Q-P),3,4)
), 0.1, 0
scale 0.35 rotate<20,-45,0>
translate P+<0.4,0.3,0>
pigment{ color rgb<1,0,0.25> } no_shadow } |
Caption "N"
+ vector: |
text{ ttf "ARIAL.TTF"
concat( "M(PQ) = (" , vstr(3,(P+Q)/2,"/",0,1) , ")"
), 0.1, 0
scale 0.35 rotate<20,-45,0>
translate (P + Q)/2 + <0.4,0.3,0>
pigment{ color Violet } no_shadow } |
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