3-d spots

If you enable Lights in the cfg configuration of a 3-d graph, the scene will be rendered by the OpenGL lighting algorithm. You can enable 1 to 8 spots of light, each is configurable (buttons l1 to l8).

Each spot has geometric properties: it may be a positional spot if w = 1 or a directional spot if w = 0

• A positional spot (w = 1) is at position x, y, z and has a direction, defined by x->, y->, z->. Light coming from a positional spot may be attenuated, the attenuation may depend on the distance between the spot and the object (with a quadratic formula, att0, att1, att2 in the spot configuration), and by the cosine of the angle between the spot direction and the segment spot-object to an exponent (exp in the spot configuration). In addition, the spot may light only inside a cone of angle configurable by the cutoff value (in degrees, use 180 for no cutoff or a value between 0 and 90). An additional attenuation comes from the cosine of the angle incoming direction-normal to the object, so that zenithal lighting is maximal.
• A directional spot w = 0 (emulating e.g. Sun light), does not attenuate (except for the angle between the direction of the spot and the normal). The direction is defined by x, y, z.

Objects from the scene may have their own properties with respect to three kinds of light:

• ambient light, emulating light coming from all directions and diffused in all directions without attenuation,
• diffuse light, emulating light coming from one direction and diffused in all directions with an attenuation factor proportionnal to the cosine of the angle of the incoming direction and the normal to the object,
• specular light, emulating light coming from one direction and reflected preferentially in the direction symmetric with respect to the normal of the object.

In addition, an object may have intrinsic light, called emission. Each property must be specified for 4 channels: r (red), b (blue) and g (green) for the colors, and a (alpha) for transparency (if you enable Blending). Object properties must be specified in their definition (on the commandline):

• gl_material=[gl_front,gl_ambient,[r,g,b,a]]
  specifies the property for ambient light, use gl_diffuse, gl_specular or gl_emission instead of gl_ambient for diffuse, specular or intrinsic light. Default is 0.2 for ambient, 0.8 for diffuse and 0 for emission on r,g,b channels and 1 on alpha channels.
• gl_material=[gl_front,gl_shininess,n]
  specifies the exponent n that will be used for specular light. The exponent is that of cos($\theta$), where $\theta$ is the angle between reflected incoming light and visualization direction (default is n = 50).
• gl_texture="filename" specify an image filename that will be mapped on a sphere or a polygon or a parametric defined surface.

Summing up, the formula for light on each channel is :

$$\sum_{{j=1}}^{8} \sum_{{j=1}}^{8} \gamma_{j}^{}$$ l =

$$\sum_{{j=1}}^{8} \alpha_{j}^{} \beta_{j}^{} {\frac{{1}}{{a_{0,j}+a_{1,j} d_j+a_{2,j} d_j^2}}}$$

where :

• o_e, o_a, o_d, o_s are the material properties with respect to ambiant, diffuse, specular light, S is the ``shininess'' (exponent for specular light)
• l_{a, j}, l_{d, j}, l_{s, j} are the properties of spot j for ambiant, diffuse and specular light
• a_{0, j}, a_{1, j}, a_{2, j} are attenuation coefficients of spot j, replaced by 1,0,0 if w = 0 (no attenuation)
• d_j is the distance of spot j to the objet
• $\alpha_{j}^{}$ is the angle between the direction of spot j and the segment from spot j and the object, except if $\alpha_{j}^{}$ is greater to the angle of cutoff of spot j ( $\alpha_{j}^{}$ = $\pi$/2), or if w = 0 ( $\alpha_{j}^{}$ = 0, no attenuation for directionnal light).
• $\beta_{j}^{}$ is the angle between the segment spot j-object and the normale to the objet (if w = 0, replace spot j-objet by the spot direction)
• $\gamma_{j}^{}$ is the angle between the symmetric of the direction of the spot w.r.t. the normal of the object and the segment object-eye