Documentation:Tutorial Section 2.1
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CSG Objects
CSG Intersection
Now let's use these same spheres to illustrate the intersection CSG
object. We change the word union to intersection and
delete the scale and rotate statements:
intersection {
sphere { <0, 0, 0>, 1
translate -0.5*x
}
sphere { <0, 0, 0>, 1
translate 0.5*x
}
pigment { Red }
}
We trace the file and will see a lens-shaped object instead of the two spheres. This is because an intersection consists of the area shared by both shapes, in this case the lens-shaped area where the two spheres overlap. We like this lens-shaped object so we will use it to demonstrate differences.
CSG Difference
We rotate the lens-shaped intersection about the y-axis so that the broad side is facing the camera.
intersection{
sphere { <0, 0, 0>, 1
translate -0.5*x
}
sphere { <0, 0, 0>, 1
translate 0.5*x
}
pigment { Red }
rotate 90*y
}
Let's create a cylinder and stick it right in the middle of the lens.
cylinder { <0, 0, -1> <0, 0, 1>, .35
pigment { Blue }
}
We render the scene to see the position of the cylinder. We will place a
difference block around both the lens-shaped intersection and
the cylinder like this:
difference {
intersection {
sphere { <0, 0, 0>, 1
translate -0.5*x
}
sphere { <0, 0, 0>, 1
translate 0.5*x
}
pigment { Red }
rotate 90*y
}
cylinder { <0, 0, -1> <0, 0, 1>, .35
pigment { Blue }
}
}
We render the file again and see the lens-shaped intersection with a neat
hole in the middle of it where the cylinder was. The cylinder has been subtracted
from the intersection. Note that the pigment of the cylinder causes the surface of the hole to
be colored blue. If we eliminate this pigment the surface of the hole will be black, as this is the default color if no color is specified.
OK, let's get a little wilder now. Let's declare our perforated lens object to give it a name. Let's also eliminate all textures in the declared object because we will want them to be in the final union instead.
#declare Lens_With_Hole = difference {
intersection {
sphere { <0, 0, 0>, 1
translate -0.5*x
}
sphere { <0, 0, 0>, 1
translate 0.5*x
}
rotate 90*y
}
cylinder { <0, 0, -1> <0, 0, 1>, .35 }
}
Let's use a union to build a complex shape composed of copies of this object.
union {
object { Lens_With_Hole translate <-.65, .65, 0> }
object { Lens_With_Hole translate <.65, .65, 0> }
object { Lens_With_Hole translate <-.65, -.65, 0> }
object { Lens_With_Hole translate <.65, -.65, 0> }
pigment { Red }
}
We render the scene. An interesting object to be sure. But let's try something more. Let's make it a partially-transparent object by adding some filter to the pigment block.
union {
object { Lens_With_Hole translate <-.65, .65, 0> }
object { Lens_With_Hole translate <.65, .65, 0> }
object { Lens_With_Hole translate <-.65, -.65, 0> }
object { Lens_With_Hole translate <.65, -.65, 0> }
pigment { Red filter .5 }
}
We render the file again. This looks pretty good... only... we can see parts of each of the lens objects inside the union! This is not good.
CSG Merge
This brings us to the fourth kind of CSG object, the merge.
Merges are the same as unions, but the geometry of the objects in the CSG
that is inside the merge is not traced. This should eliminate the problem
with our object. Let's try it.
merge {
object { Lens_With_Hole translate <-.65, .65, 0> }
object { Lens_With_Hole translate <.65, .65, 0> }
object { Lens_With_Hole translate <-.65, -.65, 0> }
object { Lens_With_Hole translate <.65, -.65, 0> }
pigment { Red filter .5 }
}
Sure enough, it does!
CSG Pitfalls
There is a severe pitfall in the CSG code that we have to be aware of.
Co-incident Surfaces
POV-Ray uses inside/outside tests to determine the points at which a ray intersects a CSG object. A problem arises when the surfaces of two different shapes coincide because there is no way (due to the computer's floating-point accuracy) to tell whether a point on the coincident surface belongs to one shape or the other.
Look at the following example where a cylinder is used to cut a hole in a larger box.
difference {
box { -1, 1 pigment { Red } }
cylinder { -z, z, 0.5 pigment { Green } }
}
Note: The vectors -1 and 1 in the box definition expand to <-1,-1,-1> and <1,1,1> respectively.
If we trace this object we see red speckles where the hole is supposed to be. This is caused by the coincident surfaces of the cylinder and the box. One time the cylinder's surface is hit first by a viewing ray, resulting in the correct rendering of the hole, and another time the box is hit first, leading to a wrong result where the hole vanishes and red speckles appear. This problem can be avoided by increasing the size of the cylinder to get rid of the coincidence surfaces. This is done by:
difference {
box { -1, 1 pigment { Red } }
cylinder { -1.001*z, 1.001*z, 0.5 pigment { Green } }
}
In general we have to make the subtracted object a little bit larger in a CSG difference. We just have to look for coincident surfaces and increase the subtracted object appropriately to get rid of those surfaces.
The same problem occurs in CSG intersections and is also avoided by scaling some of the involved objects.
The Light Source
In any ray-traced scene, the light needed to illuminate our objects and their surfaces must come from a light source. There are many kinds of light sources available in POV-Ray and careful use of the correct kind can yield very impressive results. Let's take a moment to explore some of the different kinds of light sources and their various parameters.
The Pointlight Source
Pointlights are exactly what the name indicates. A pointlight has no size, is invisible and illuminates everything in the scene equally no matter how far away from the light source it may be (this behavior can be changed). This is the simplest and most basic light source. There are only two important parameters, location and color. Let's design a simple scene and place a pointlight source in it.
We create a new file and name it litedemo.pov. We edit it as
follows:
#include "colors.inc"
#include "textures.inc"
camera {
location <-4, 3, -9>
look_at <0, 0, 0>
angle 48
}
We add the following simple objects:
plane {
y, -1
texture {
pigment {
checker
color rgb<0.5, 0, 0>
color rgb<0, 0.5, 0.5>
}
finish {
diffuse 0.4
ambient 0.2
phong 1
phong_size 100
reflection 0.25
}
}
}
torus {
1.5, 0.5
texture { Brown_Agate }
rotate <90, 160, 0>
translate <-1, 1, 3>
}
box {
<-1, -1, -1>, <1, 1, 1>
texture { DMFLightOak }
translate <2, 0, 2.3>
}
cone {
<0,1,0>, 0, <0,0,0>, 1
texture { PinkAlabaster }
scale <1, 3, 1>
translate <-2, -1, -1>
}
sphere {
<0,0,0>,1
texture { Sapphire_Agate }
translate <1.5, 0, -2>
}
Now we add a pointlight:
light_source {
<2, 10, -3>
color White
}
We render this and see that the objects are clearly visible with sharp shadows. The sides of curved objects nearest the light source are brightest in color with the areas that are facing away from the light source being darkest. We also note that the checkered plane is illuminated evenly all the way to the horizon. This allows us to see the plane, but it is not very realistic.
The Spotlight Source
Spotlights are a very useful type of light source. They can be used to add
highlights and illuminate features much as a photographer uses spots to do
the same thing. To create a spotlight simply add the spotlight
keyword to a regular point light. There are a few more parameters with
spotlights than with pointlights. These are radius,
falloff, falloff and point_at. The radius parameter is the angle of the fully illuminated cone. The falloff parameter is the angle of the umbra cone where the light falls off to darkness. The tightness is a parameter that determines the rate of the light falloff. The point_at parameter is just what it says, the location where the spotlight is pointing to. Let's change the light in our scene as follows:
light_source {
<0, 10, -3>
color White
spotlight
radius 15
falloff 20
tightness 10
point_at <0, 0, 0>
}
We render this and see that only the objects are illuminated. The rest of the plane and the outer portions of the objects are now unlit. There is a broad falloff area but the shadows are still razor sharp. Let's try fiddling with some of these parameters to see what they do. We change the falloff value to 16 (it must always be larger than the radius value) and render again. Now the falloff is very narrow and the objects are either brightly lit or in total darkness. Now we change falloff back to 20 and change the tightness value to 100 (higher is tighter) and render again. The spotlight appears to have gotten much smaller but what has really happened is that the falloff has become so steep that the radius actually appears smaller.
We decide that a tightness value of 10 (the default) and a falloff value of 18 are best for this spotlight and we now want to put a few spots around the scene for effect. Let's place a slightly narrower blue and a red one in addition to the white one we already have:
light_source {
<10, 10, -1>
color Red
spotlight
radius 12
falloff 14
tightness 10
point_at <2, 0, 0>
}
light_source {
<-12, 10, -1>
color Blue
spotlight
radius 12
falloff 14
tightness 10
point_at <-2, 0, 0>
}
Rendering this we see that the scene now has a wonderfully mysterious air to it. The three spotlights all converge on the objects making them blue on one side and red on the other with enough white in the middle to provide a balance.
The Cylindrical Light Source
Spotlights are cone shaped, meaning that their effect will change with
distance. The farther away from the spotlight an object is, the larger the
apparent radius will be. But we may want the radius and falloff to be a
particular size no matter how far away the spotlight is. For this reason,
cylindrical light sources are needed. A cylindrical light source is just like
a spotlight, except that the radius and falloff regions are the same no
matter how far from the light source our object is. The shape is therefore a
cylinder rather than a cone. We can specify a cylindrical light source by
replacing the spotlight keyword with the cylinder
keyword. We try this now with our scene by replacing all three spotlights
with cylinder lights and rendering again. We see that the scene is much
dimmer. This is because the cylindrical constraints do not let the light
spread out like in a spotlight. Larger radius and falloff values are needed
to do the job. We try a radius of 20 and a falloff of 30 for all three
lights. That's the ticket!
The Area Light Source
So far all of our light sources have one thing in common. They produce sharp shadows. This is because the actual light source is a point that is infinitely small. Objects are either in direct sight of the light, in which case they are fully illuminated, or they are not, in which case they are fully shaded. In real life, this kind of stark light and shadow situation exists only in outer space where the direct light of the sun pierces the total blackness of space. But here on Earth, light bends around objects, bounces off objects, and usually the source has some dimension, meaning that it can be partially hidden from sight (shadows are not sharp anymore). They have what is known as an umbra, or an area of fuzziness where there is neither total light or shade. In order to simulate these soft shadows, a ray-tracer must give its light sources dimension. POV-Ray accomplishes this with a feature known as an area light.
Area lights have dimension in two axis'. These are specified by the
first two vectors in the area light syntax. We must also specify how many
lights are to be in the array. More will give us cleaner soft shadows but
will take longer to render. Usually a 3*3 or a 5*5 array will suffice. We
also have the option of specifying an adaptive value. The
adaptive keyword tells the ray-tracer that it can adapt to the
situation and send only the needed rays to determine the value of the pixel.
If adaptive is not used, a separate ray will be sent for every light in the
area light. This can really slow things down. The higher the adaptive value
the cleaner the umbra will be but the longer the trace will take. Usually an
adaptive value of 1 is sufficient. Finally, we probably should use the
jitter keyword. This tells the ray-tracer to slightly move the
position of each light in the area light so that the shadows appear truly
soft instead of giving us an umbra consisting of closely banded shadows.
OK, let's try one. We comment out the cylinder lights and add the following:
light_source {
<2, 10, -3>
color White
area_light <5, 0, 0>, <0, 0, 5>, 5, 5
adaptive 1
jitter
}
This is a white area light centered at <2,10,-3>. It is 5 units (along the x-axis) by 5 units (along the z-axis) in size and has 25 (5*5) lights in it. We have specified adaptive 1 and jitter. We render and right away we notice two things. The trace takes quite a bit longer than it did with a point or a spotlight and the shadows are no longer sharp! They all have nice soft umbrae around them. Wait, it gets better.
Spotlights and cylinder lights can be area lights too! Remember those sharp shadows from the spotlights in our scene? It would not make much sense to use a 5*5 array for a spotlight, but a smaller array might do a good job of giving us just the right amount of umbra for a spotlight. Let's try it. We comment out the area light and change the cylinder lights so that they read as follows:
light_source {
<2, 10, -3>
color White
spotlight
radius 15
falloff 18
tightness 10
area_light <1, 0, 0>, <0, 0, 1>, 2, 2
adaptive 1
jitter
point_at <0, 0, 0>
}
light_source {
<10, 10, -1>
color Red
spotlight
radius 12
falloff 14
tightness 10
area_light <1, 0, 0>, <0, 0, 1>, 2, 2
adaptive 1
jitter
point_at <2, 0, 0>
}
light_source {
<-12, 10, -1>
color Blue
spotlight
radius 12
falloff 14
tightness 10
area_light <1, 0, 0>, <0, 0, 1>, 2, 2
adaptive 1
jitter
point_at <-2, 0, 0>
}
We now have three area-spotlights, one unit square consisting of an array of four (2*2) lights, three different colors, all shining on our scene. We render this and it appears to work perfectly. All our shadows have small, tight umbrae, just the sort we would expect to find on an object under a real spotlight.
The Ambient Light Source
The ambient light source is used to simulate the effect of
inter-diffuse reflection. If there was not inter-diffuse reflection all
areas not directly lit by a light source would be completely dark. POV-Ray
uses the ambient keyword to determine how much light coming from
the ambient light source is reflected by a surface.
By default the ambient light source, which emits its light everywhere and in
all directions, is pure white (rgb <1,1,1>). Changing its
color can be used to create interesting effects. First of all the overall
light level of the scene can be adjusted easily. Instead of changing all
ambient values in every finish only the ambient light source is modified. By
assigning different colors we can create nice effects like a moody reddish
ambient lighting.
Below is an example of a red ambient light source.
global_settings { ambient_light rgb<1, 0, 0> }
See Ambient Light for more details.
Light Source Specials
Using Shadowless Lights
Light sources can be assigned the shadowless keyword and no
shadows will be cast due to its presence in a scene. Sometimes, scenes are
difficult to illuminate properly using the lights we have chosen to
illuminate our objects. It is impractical and unrealistic to apply a higher
ambient value to the texture of every object in the scene. So instead, we
would place a couple of fill lights around the scene. Fill lights
are simply dimmer lights with the shadowless keyword that act to
boost the illumination of other areas of the scene that may not be lit well.
Let's try using one in our scene.
Remember the three colored area spotlights? We go back and un-comment them and comment out any other lights we have made. Now we add the following:
light_source {
<0, 20, 0>
color Gray50
shadowless
}
This is a fairly dim light 20 units over the center of the scene. It will give a dim illumination to all objects including the plane in the background. We render it and see.
Assigning an Object to a Light Source
Light sources are invisible. They are just a location where the light
appears to be coming from. They have no true size or shape. If we want our
light source to be a visible shape, we can use the looks_like
keyword. We can specify that our light source can look like any object we
choose. When we use looks_like, then no_shadow is
applied to the object automatically. This is done so that the object will not
block any illumination from the light source. If we want some blocking to
occur (as in a lamp shade), it is better to simply use a union to do the same
thing. Let's add such an object to our scene. Here is a light bulb we
have made just for this purpose:
#declare Lightbulb = union {
merge {
sphere { <0,0,0>,1 }
cylinder {
<0,0,1>, <0,0,0>, 1
scale <0.35, 0.35, 1.0>
translate 0.5*z
}
texture {
pigment {color rgb <1, 1, 1>}
finish {ambient .8 diffuse .6}
}
}
cylinder {
<0,0,1>, <0,0,0>, 1
scale <0.4, 0.4, 0.5>
texture { Brass_Texture }
translate 1.5*z
}
rotate -90*x
scale .5
}
Now we add the light source:
light_source {
<0, 2, 0>
color White
looks_like { Lightbulb }
}
Rendering this we see that a fairly believable light bulb now illuminates the scene. However, if we do not specify a high ambient value, the light bulb is not lit by the light source. On the plus side, all of the shadows fall away from the light bulb, just as they would in a real situation. The shadows are sharp, so let's make our bulb an area light:
light_source {
<0, 2, 0>
color White
area_light <1, 0, 0>, <0, 1, 0>, 2, 2
adaptive 1
jitter
looks_like { Lightbulb }
}
We note that we have placed this area light in the x-y-plane instead of the x-z-plane. We also note that the actual appearance of the light bulb is not affected in any way by the light source. The bulb must be illuminated by some other light source or by, as in this case, a high ambient value.
Using Light Fading
If it is realism we want, it is not realistic for the plane to be evenly
illuminated off into the distance. In real life, light gets scattered as it
travels so it diminishes its ability to illuminate objects the farther it
gets from its source. To simulate this, POV-Ray allows us to use two
keywords: fade_distance, which specifies the distance at which
full illumination is achieved, and fade_power, an exponential
value which determines the actual rate of attenuation. Let's apply these
keywords to our fill light.
First, we make the fill light a little brighter by changing
Gray50 to Gray75. Now we change that fill light as
follows:
light_source {
<0, 20, 0>
color Gray75
fade_distance 5
fade_power 1
shadowless
}
This means that the full value of the fill light will be achieved at a distance of 5 units away from the light source. The fade power of 1 means that the falloff will be linear (the light falls off at a constant rate). We render this to see the result.
That definitely worked! Now let's try a fade power of 2 and a fade distance of 10. Again, this works well. The falloff is much faster with a fade power of 2 so we had to raise the fade distance to 10.
Simple Texture Options
The pictures rendered so far where somewhat boring regarding the appearance of the objects. Let's add some fancy features to the texture.
Surface Finishes
One of the main features of a ray-tracer is its ability to do interesting
things with surface finishes such as highlights and reflection. Let's add
a nice little Phong highlight (shiny spot) to a sphere. To do this we need to
add a finish keyword followed by a parameter. We change the
definition of the sphere to this:
sphere {
<0, 1, 2>, 2
texture {
pigment { color Yellow } //Yellow is pre-defined in COLORS.INC
finish { phong 1 }
}
}
We render the scene. The phong keyword adds a highlight the same color of the light shining on the object. It adds a lot of credibility to the picture and makes the object look smooth and shiny. Lower values of phong will make the highlight less bright (values should be between 0 and 1).
| CSG Union | Adding Bumpiness |
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This document is protected, so submissions, corrections and discussions should be held on this documents talk page. |