User:Le Forgeron/nurbs - Revision history

Le Forgeron: /* Drawing a nurbs */

2018-09-02T08:31:23Z

Drawing a nurbs

Le Forgeron at 14:54, 19 August 2018

2018-08-19T14:54:17Z

Le Forgeron: /* Nurbs */

2018-07-04T08:10:03Z

Nurbs

Le Forgeron: /* Nurbs */

2018-07-04T08:08:17Z

Nurbs

Le Forgeron: /* Nurbs */

2018-07-04T08:06:56Z

Nurbs

Le Forgeron: /* Drawing a nurbs or any other UVMeshable objects */

2018-07-04T07:59:51Z

Drawing a nurbs or any other UVMeshable objects

Le Forgeron: Created page with "{{User:Le_Forgeron/HgPovray38/soon}} == Nurbs == '''nurbs''' is like '''spline''' : an invisible object NURBS means Non Uniform Rational B-Spline. syntax is

 nurbs {..."

2018-07-04T07:57:08Z

Created page with "{{User:Le_Forgeron/HgPovray38/soon}} == Nurbs == '''nurbs''' is like '''spline''' : an invisible object NURBS means Non Uniform Rational B-Spline. syntax is <pre> nurbs {..."

New page

{{User:Le_Forgeron/HgPovray38/soon}}

== Nurbs ==

'''nurbs''' is like '''spline''' : an invisible object

NURBS means Non Uniform Rational B-Spline.

syntax is
<pre>
nurbs {
Uorder, Vorder,
Usize, Vsize
UKNOTS
VKNOTS
ULINE (repeated Vsize time)
[OBJECTS_MODIFIERS...]
}

ULINE := WEIGHTED_POINT (repeated Usize time)
WEIGHTED_POINT := < X, Y, Z, W >
UKNOTS := KNOT, (repeated Uorder+Usize time)
VKNOTS := KNOT, (repeated Vorder+Vsize time)
KNOT := float value
</pre>

* The `order` must be at least 2 and at most `size` for each U & V coordinates.
* Along a sequence of knots, the values must not be decreasing.
* '''nurbs''' is one of the UVMeshable objects

=== Drawing a nurbs or any other UVMeshable objects ===

<source lang="pov">
#version 3.7;
global_settings{ assumed_gamma 1.0 }

#declare UVMeshableObject = nurbs { 3,3,7,7
// u knots
0, 0, 0, 1/5, 2/5, 3/5, 4/5, 1, 1, 1
// v knots
0, 0, 0, 1/5, 2/5, 3/5, 4/5, 1, 1, 1
// first line of (x,y,z,w)
<-4.1894,-5.4790,0.0000,1.0000> <-4.1894,-4.3181,2.0249,1.0000>
<-4.1894,-2.8825,0.0000,1.0000> <-4.1894,-1.5000,0.0000,1.0000>
<-4.1894,-0.5000,0.0000,1.0000> <-4.1894,0.5000,0.0000,1.0000>
<-4.1894,1.5000,0.0000,1.0000>

// second line of (x,y,z,w)
<-2.6808,-4.8585,0.6794,1.0000>
<-2.6808,-4.3181,2.0249,1.0000> <-2.6808,-2.8825,0.0000,1.0000>
<-2.6808,-1.5000,3.2519,1.0000> <-2.6808,-0.5000,0.0000,1.0000>
<-2.6808,0.5000,0.0000,1.0000> <-2.6808,1.5000,3.2103,1.0000>

// third line of (x,y,z,w)
<-1.5000,-5.4790,0.0000,1.0000>
<-1.5000,-4.3181,2.0249,1.0000> <-1.5000,-2.8825,0.0000,1.0000>
<-1.5000,-1.5000,0.0000,1.0000> <-1.5000,-0.5000,1.2319,1.0000>
<-1.5000,0.5000,0.0000,1.0000> <-1.5000,1.5000,0.0000,1.0000>

// fourth line of (x,y,z,w)
<-0.5000,-5.4790,0.0000,1.0000>
<-0.5000,-4.3181,0.0000,1.0000> <-0.5000,-2.8825,1.7624,1.0000>
<-0.5000,-1.5000,0.0000,1.0000> <-0.5000,-0.5000,1.0000,1.0000>
<-0.5000,0.5000,1.0000,1.0000> <-0.5000,1.5000,0.0000,1.0000>

// fifth line of (x,y,z,w)
<0.5000,-5.4790,0.0000,1.0000>
<0.5000,-4.3181,0.0000,1.0000> <0.5000,-2.8825,0.0000,1.0000>
<0.5000,-1.5000,1.1552,1.0000> <0.5000,-0.5000,1.0000,1.0000>
<0.5000,0.5000,1.0000,1.0000> <0.5000,1.5000,0.0000,1.0000>

// sixth line of (x,y,z,w)
<1.5000,-5.4790,1.9780,1.0000>
<1.5000,-4.3181,0.0000,1.0000> <1.5000,-2.8825,1.7335,1.0000>
<1.5000,-1.5000,0.0000,1.0000> <1.5000,-0.5000,0.0000,1.0000>
<1.5000,0.5000,0.0000,1.0000> <1.5000,1.5000,1.5217,1.0000>

// seventh line of (x,y,z,w)
<2.9668,-5.4790,-0.2469,1.0000>
<2.9668,-4.3181,0.0000,1.0000> <2.9668,-2.8825,0.0000,1.0000>
<2.9668,-1.5000,0.0000,1.0000> <2.9668,-0.5000,-2.9599,1.0000>
<2.9668,0.5000,0.0000,1.0000> <2.9668,1.5000,0.0000,1.0000>
};

#declare Texture = texture { checker texture { pigment { color blue 1 } } texture { pigment { color rgb <1,1,0> } } }

#include "NurbsMesh.inc"
#declare UResolution = 92;
#declare VResolution = 92;
mesh {
UVMeshable( UVMeshableObject, UResolution, VResolution )
texture { uv_mapping Texture scale <1/24, 1/24, 1> }
}

light_source {+40*z+90*x, 1 }
camera { location uv_vertex( UVMeshableObject, 0.5, 0.5 ) +<0,0,40>
direction z
up y
right image_width/image_height*x
look_at uv_vertex( UVMeshableObject, 0.5, 0.5 )
angle 16
}
</source>

[[Image:LeForgeronNurbs.png| "Nurbs"]]

← Older revision		Revision as of 08:31, 2 September 2018
Line 105:		Line 105:

	[[Image:LeForgeronNurbs.png\| Nurbs]]		[[Image:LeForgeronNurbs.png\| Nurbs]]
		+
		+	=== closed nurbs ===
		+
		+	Closed nurbs are achieved by having some special arrangement for the control points and knot sequence. For example, the knot sequence [ 0., 0., 0., 0., 0.25, 0.5, 0.75, 1.0, 1.0, 1.0, 1.0] with 7 control points (P1, P2,...to P7) will result in an open cubic B-spline curve (when the order is 3). If we change the knot sequence into [ -0.75, -0.5, -0.25, 0., 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75] and make P5=P1, P6=P2 and P7=P3, then the curve will become a closed cubic B-spline curve with C2 continuity at the joint.
		+
		+	[[Image:LeForgeronTorusNurbs.png\| Nurbs illustration]]
		+
		+	<source lang="pov">
		+	#version 3.7;
		+	#global_settings{ max_trace_level 10 assumed_gamma 1.0 }
		+	#include "finish.inc"
		+	#declare Major=6;// Major radius of torus
		+	#declare Minor=5;// Minor radius of torus
		+	#declare MAX=5;// max order of nurbs to draw
		+	#declare SPACE=(Major+Minor)*1.404;// Room around each object (radius)
		+	#declare PTI=10;// number of minor circles along the major radius
		+	#declare PTJ=4;// number of points on each minor circle
		+	#declare RESOLUTION=64;// resolution of the mesh
		+
		+
		+	camera { orthographic
		+	location 130y+SPACE(MAX+1)(x-z)-zSPACE
		+	direction -y
		+	up (1+(MAX-1)SPACE)z*2
		+	right (1+(MAX-1)SPACE)2ximage_width/image_height
		+	}
		+
		+	#declare T = texture { pigment { uv_mapping checker
		+	pigment{ color srgb <1,1,0> transmit 0.0 filter 0 }
		+	pigment{ color srgb <0,1,1> transmit 0.0 filter 0 }
		+	scale <1/4,1/4,1>
		+	} };
		+
		+	light_source { 10y-10x, 0.8 scale 10}
		+	light_source { 10y-10z, 2/3 scale 10}
		+	light_source { 10*y, 1/3 scale 10}
		+	light_source { -10*z, 1/3 scale 10}
		+
		+	#macro P(I,J)
		+	#local V=(mod(I,2)Minor+Major)x+(Minor)<cos(pi2J/PTJ),sin(pi2*J/PTJ),0>;
		+	#local W=vrotate(V, 360I/(PTI)y);
		+	W
		+	#end
		+
		+	#macro NURBS(OrderU, OrderV)
		+	nurbs{
		+	OrderU, OrderV,
		+	#declare NBI=PTI+OrderU-1;
		+	#declare NBJ=PTJ+OrderV-1;
		+	NBI, NBJ,
		+	#for(I,1,NBI+OrderU)
		+	I,
		+	#end
		+	#for(J,1,NBJ+OrderV)
		+	J,
		+	#end
		+	#for(J,1,NBJ)
		+	#for(I,1,NBI)
		+	#declare W= P(I,J);
		+	<W.x,W.y,W.z,1>
		+	#end
		+	#end
		+	}
		+	#end
		+
		+
		+	#include "NurbsMesh.inc"
		+	#for(X,2,MAX)
		+	#for(Y,2,MAX)
		+	#declare Nurbs=NURBS(X,Y);
		+	mesh {
		+	UVMeshable( Nurbs, RESOLUTION, RESOLUTION )
		+	texture { T } translate SPACE2(Xx-Yz)
		+	}
		+	#end
		+	#end
		+
		+	#declare UN= union{
		+	#for(J,1,NBJ)
		+	#for(I,1,NBI)
		+	#declare W=P(I,J);
		+	sphere {W, 0.2 texture { pigment { color srgb <1,0,0>}}}
		+	#declare OLD=W;
		+	#declare W=P(I,J+1);
		+	cylinder{OLD,W,0.1 texture { pigment { color srgb <0,1,0>}}}
		+	#declare W=P(I+1,J);
		+	cylinder{OLD,W,0.1 texture { pigment { color srgb <0,0,1>}}}
		+	#end
		+	#end
		+	}
		+
		+	object { UN translate SPACE2(x-2*z) }
		+	object { UN rotate 90x translate SPACE2(x-4z) }
		+	plane{ y,-Minor*2 texture { pigment { color srgb 0.5 } } }
		+
		+	</source>

← Older revision		Revision as of 14:54, 19 August 2018
Line 1:		Line 1:
−	{{User:Le_Forgeron/HgPovray38/~~soon~~}}	+	{{User:Le_Forgeron/HgPovray38/available}}

@@ Line 4: / Line 4: @@
 == Nurbs ==
-'''nurbs''' is like '''spline''' : an invisible object
+<code>nurbs</code> is like <code>spline</code> : an invisible object
 NURBS means Non Uniform Rational B-Spline.
@@ Line 26: / Line 26: @@
 </pre>
-* The <code>order</code> must be at least 2 and at most `size` for each U & V coordinates.
+* The '''order''' must be at least 2 and at most `size` for each U & V coordinates.
-* Along a sequence of knots, the values must not be decreasing.
+* Along a sequence of knots, the values must not be decreasing: the next value can be the same or bigger.
-* '''nurbs''' is one of the [[User:Le_Forgeron/UVMeshable|UVMeshable]] objects
+* <code>nurbs</code> is one of the [[User:Le_Forgeron/UVMeshable|UVMeshable]] objects
 === Drawing a nurbs ===

@@ Line 28: / Line 28: @@
 * The <code>order</code> must be at least 2 and at most `size` for each U & V coordinates.
 * Along a sequence of knots, the values must not be decreasing.
-* '''nurbs''' is one of the UVMeshable objects
+* '''nurbs''' is one of the [[User:Le_Forgeron/UVMeshable|UVMeshable]] objects
 === Drawing a nurbs ===

@@ Line 30: / Line 30: @@
 * '''nurbs''' is one of the UVMeshable objects
-=== Drawing a nurbs or any other UVMeshable objects ===
+=== Drawing a nurbs ===
 <source lang="pov">
@@ Line 104: / Line 104: @@
 </source>
-[[Image:LeForgeronNurbs.png| "Nurbs"]]
+[[Image:LeForgeronNurbs.png| Nurbs]]