I’M BLINDED!

Or

Other types of light


“Point me to the right direction…”

get it? point like point light, but direction like directional light? ....
.. ah forget it.

Other than point lights, we have two other types of lights in OGRE:

  • Directional lights: have no position, only a direction.
  • Spotlights: these lights have a ‘corridor cone’ in a direction. They have two cones:
    • Inner cone: maximum illumination.
    • Outer cone: gradually fading illumination.

Directional lights

These lights are probably the easiest thing in the world to calculate. All they have is a direction from which they are coming from (as if originating from infinity and traveling parallel).

All you have to do is ignore the position. That means we have one less calculation. There isn’t much more to tell, just show you the code (even that is redundant). OGRE sends directional lights' direction (xyz) instead of position, with the w component set to 0.

vertexOut mainVS(vertexIn input)
{
	vertexOut output = (vertexOut)0;
	
	float4 worldPos = mul(input.pos, world_m);
	//fill output
	//------------------------------
	output.pos 	= mul(input.pos, worldViewProj_m);
	output.normal 	= mul(input.normal, world_m);
	output.viewDir	= viewPos - worldPos;
	//------------------------------
	return output;
}

float4 mainPS(vertexOut input) : COLOR 
{
	//normalize per pixel
	//------------------------------
	float3 normal 	= normalize(input.normal);
	float3 viewDir 	= normalize(input.viewDir);
	//------------------------------
	//diff and specular
	//------------------------------
	float 	dotNL 	= dot(lightPos.xyz, normal);
	float4	diff    = saturate(dotNL);
	
	float3 	halfAng = normalize(viewDir + lightPos.xyz);
	float 	dotNH	= dot(normal, halfAng);
	float 	spec	= pow(saturate(dotNH),50);
	//------------------------------
	
	return  diff*diffColor + spec*specColor + ambientColor ;
}

Spotlights

Spot lights are a bit more complicated, since they originate from a specific point, project to a specific direction, and have a cone which only in it the object is affected (like a flash light). These points make it somewhat trickier.

Let’s take a look at the spotlight:
Image

To avoid confusion, we will rename lightDir to pixelToLight since the spotlight has a facing direction.

We will use two dot products:

  • dotNL : dot between pixelToLight and the surface normal
  • dotPLd: dot between the inverse pixelToLight and spotlight direction


We have a few more variables however; when you ask for spotlight_params from OGRE material script, OGRE will send a float4 organized as such:

  • cos(innerConeAngle/2)
  • cos(outerConeAngle/2)
  • falloff value
  • 1


The forth value (w component) is used to help differentiate spotlights from point lights.

The cosine uses the half of the angle because the angle defines the cone, and we need only the angle between the side of the cone and the axis (which is the spotlight facing vector).

Calculating

There are two parts for determining the effect of the cone of light on the object depending on its direction to it:

  1. The dotNL must be positive: because otherwise we are either behind the light or on the other side of the object.
  2. The dotPLd value:
  • The value of the dotPLd equals in value to the cosine between the spotlight facing vector and pixelToLight; since we have the cosine of the angle between the cones' side and their axis (which is the spotlight facing vector) comparing dotPLd with these number is essentially comparing its angle with the cones' (if you look at the drawing again, the angle of the dotPLd is smaller than both cones meaning it lies within the inner cone, while the farthest pixel on the sphere is in the outer cone)
  • Diffuse:
    • Larger than cos(innerConeAngle/2): the pixel is in the inner cone.
      • Value: the diffuse will equal the dotNL.
    • Larger than cos(outerConeAngle/2): the pixel is in the outer cone.
      • Value: the diffuse will equal the dotNL, multiplied by the relative location of the pixel between the outer and inner cone (will be explained later)
    • Otherwise: not in the spotlight’s AOE.
  • Specular:
    • As long as the dotPLd is positive, the specular is present; this is because the specular reflects the source of the light, which means that as long as pixel is not behind it, the specular will appear.


I ignore the falloff value, because I don’t really know what to do with it.

Code

The vertex program remained almost unchanged, but take a look at it anyhow:

vertexOut mainVS(vertexIn input)
{
	vertexOut output = (vertexOut)0;
	
	float4 worldPos 	= mul(input.pos, world_m);
	//fill output
	//------------------------------
	output.pos 		= mul(input.pos, worldViewProj_m);
	output.normal 		= mul(input.normal, world_m);
	output.pixelToLight	= lightPos - worldPos;
	output.viewDir		= viewPos - worldPos;
	//------------------------------
	return output;
}


The main change is in the pixel program:
We begin the program by normalizing and preparing the dot products:

float4 mainPS(vertexOut input) : COLOR 
{
	//prep
	//------------------------------
	float3 normal 		= normalize(input.normal);
	float3 pixelToLight	= normalize(input.pixelToLight);
	float3 viewDir 		= normalize(input.viewDir);

	float 	dotPLd	= dot(-pixelToLight, spotLightDir);
	float 	dotNL 	= dot(pixelToLight, normal);
	//------------------------------


Now, let’s add the diffuse and specular as we described earlier and return the value:

// lights
	//------
	float4	diff = 0, spec = 0;
	if(dotNL > 0)
	{	
		//diffuse
		//------------------------------
		if	( dotPLd > spotLightParams.x )
			diff 	= dotNL;
		else 
		if	( dotPLd > spotLightParams.y )
			diff 	= dotNL * (1-(spotLightParams.x - dotPLd)/(spotLightParams.x - spotLightParams.y));
		//------------------------------
		// specular
		//------------------------------
		if (dotPLd > 0) 
		{
			float3 	halfAng = normalize(viewDir + pixelToLight);
			float 	dotNH	= dot(normal, halfAng);
			spec 	= pow(saturate(dotNH),100);
		}
		//------------------------------
	}
	//------
	return  diff*diffColor + spec*specColor;
}

Outer cone diffuse explained

Why

dotNL * (1-(spotLightParams.x - dotPLd)/(spotLightParams.x - spotLightParams.y));

You ask?
We need to know where the pixel is between the inner and outer cones, but in a relative value (range of 0 to 1).
Therefore, we must first do this:

spotLightParams.x – dotPLd


This will give us the absolute difference between the dotPLd (the orthogonal to pixelToLight) and the inner cone limit.

In order to receive a relative value, we divide it by the absolute difference between the inner cone limit and the outer cone limit:

(spotLightParams.x - dotPLd)/(spotLightParams.x - spotLightParams.y)


The problem is that the value is inversed (closest will equal 0) so we need to one minus it:

(1-(spotLightParams.x - dotPLd)/(spotLightParams.x - spotLightParams.y))


And finally, we need to address the angle towards the source of the light (dotNL):

dotNL * (1-(spotLightParams.x - dotPLd)/(spotLightParams.x - spotLightParams.y))

Differentiating light types

When you ask for light data from OGRE material script, you will receive all lights depending on distance, therefore, you don’t know if it’s a point light, a directional light or a spotlight.

In order to address all three in one shader, we need to know how to differ them; we need three things from the material script:

  • Light_position_array
  • light_direction_array
  • spotlight_params


Each type of light has a different signature (a different combination of values):
Point light:

  • light_position : (pos.x, pos.y, pos.z, 1)
  • light_direction : not relevant
  • spotlight_params : (1, 0, 0, 1)


Directional light:

  • light_position : (-dir.x, -dir.y,-dir.z, 0)
  • light_direction : not relevant
  • spotlight_params : (1, 0, 0, 1)


Spotlight:

  • light_position : (pos.x, pos.y, pos.z, 1)
  • light_direction : (dir.x, dir.y, dir.z )
  • spotlight_params : (cos(innerAngle/2) , cos(outerAngle/2) , falloff, 1)

“Why is light_direction not relevant in directional light?”

Because it is deprecated for greater flexibility. Instead, its inverse direction is sent in light_position, with the w component set to 0 to differ it from point or spot light.

The only reason it’s not deprecated in spotlights is that they have both direction and position.

Completionist

As a closing note, lets write a shader that an handle multiple lights of any type!
Try and write it on your own, and don’t give up – it mihgt take a while.
Tips:

  • efficiency is key : try and avoid unnecessary work
  • Delegate: write sub programs to do the main bulk of the code separately, and leave the work flow in the main program.
  • Shader model 3: if the program gets large, you might have to use ps_3_0 and vs_3_0 (otherwise you'll pass the instruction limit).
  • Work slowly: do each task at a time; expand on need – make sure what you already wrote works.

My solution

I wrote my own version for this; it’s a bit more mature than what we wrote up to this point, but all of its elements should be familiar to you. Just follow the work flow line by line (starting with the main programs) and you’ll get it.

A few words about it:

  • all positions and directions in object space, saving time (spent on transforming before calculating directional vectors) and also helps result accuracy.
  • Use of shader model 3.
  • Use of inout for the sub programs to make them as seamless with the main program as possible.
  • Use of light_distance_object_space instead of manual calculation (trading attenuation accuracy for speed)


material:

vertex_program lightMasterA_VS hlsl
{
	source lightmaster.hlsl
	target vs_3_0
	entry_point multiTypeLightVS
	preprocessor_defines lightCount=5
	default_params
	{
		param_named_auto 	worldViewProj_m 	worldviewproj_matrix
		param_named_auto	cameraPos		camera_position_object_space
		param_named_auto	lightPoses		light_position_object_space_array	5
	}
}

fragment_program lightMasterA_PS hlsl
{
	source lightmaster.hlsl
	target ps_3_0
	entry_point multiTypeLightPS
	preprocessor_defines lightCount=5
	default_params
	{
		param_named_auto	lightDirs		light_direction_object_space_array 	5
		param_named_auto	SLParamsArray		spotlight_params_array			5
		param_named_auto	diffColors		light_diffuse_colour_array		5
		param_named_auto	specColors		light_specular_colour_array		5
		param_named_auto	lightAttens		light_attenuation_array			5
		param_named_auto	lightDists		light_distance_object_space_array	5
		param_named_auto	ambientColor		ambient_light_colour
		param_named specShine float 55
	}
}

material lightMasterA
{
	technique
	{
		pass
		{
			vertex_program_ref lightMasterA_VS {}
			fragment_program_ref lightMasterA_PS {}
		}
	}
}


the HLSL file:

struct vertexIn
{
	float4 position : POSITION;
	float3 normal	: NORMAL0;
};
 
struct vertexOut
{
	float4 position  		: POSITION;
	float3 normal			: TEXCOORD0;
	float3 viewDir   		: TEXCOORD1;
	float3 pixelToLight[lightCount]	: TEXCOORD2;
};
 
//lighting sub program, read multiTypeLightPS first(this one is called from it)
//--------------------------------------------------------------------------------
void light(	float3 normal, 
		float3 viewDir, 
		float3 pixelToLight,
		float3 spotLightDir,
		float4 spotLightParams,
		float4 diffColor,
		float4 specColor,
		float4 lightAtten,
		float  lightDist,
		float  specShine,
	inout	float4 diff,
	inout	float4 spec
	)
{
	float 	dotNL	 	= dot(pixelToLight, normal);
	float 	luminosity 	= 1 / ( lightAtten.y + lightAtten.z*lightDist + lightAtten.w*pow(lightDist,2));
	float3 	halfAng 	= normalize(viewDir + pixelToLight);
	float 	dotNH		= dot(normal, halfAng);
		
	// if spotlight params are (1, 0, 0, 1) we have a point, directional or empty light; we handle them the same.
	if(spotLightParams.x == 1 && spotLightParams.y == 0 && spotLightParams.z == 0 && spotLightParams.w == 1)
	{
		spec	+= pow(saturate(dotNH),specShine) * specColor * luminosity;
		diff 	+= (saturate(dotNL)) * diffColor * luminosity;		
	}
	else
	if(dotNL > 0)
	{	
		//if it was not either of the above, we have a spotlight
		float 	dotPLd		= dot(-pixelToLight, spotLightDir);
		//diffuse
		//------------------------------
		if	( dotPLd > spotLightParams.y )
			diff += dotNL * (1-(spotLightParams.x - dotPLd)/(spotLightParams.x - spotLightParams.y)) * diffColor * luminosity;
		else
		if	( dotPLd > spotLightParams.x )
			diff += dotNL * diffColor * luminosity;	
		//------------------------------

		// specular
		//------------------------------
		if (dotPLd > 0) 
			spec 	+= pow(saturate(dotNH),specShine) * specColor * luminosity;
		//------------------------------
	}
}
//--------------------------------------------------------------------------------
 
// main vertex program
//--------------------------------------------------------------------------------
vertexOut multiTypeLightVS(	vertexIn 	input,
			uniform	float4x4 	worldViewProj_m,
			uniform	float4 		cameraPos,
			uniform	float4 		lightPoses[lightCount]
			)
{
	vertexOut output= (vertexOut)0;
	
	output.position = mul(worldViewProj_m, input.position);
	output.normal 	= input.normal;
	output.viewDir	= cameraPos - input.position;
	int j = 2;
	
	for(int i = 0; i < lightCount; i++)
	{	
		if(lightPoses[i].w == 0)
			output.pixelToLight[i] = lightPoses[i].xyz;
		else
			output.pixelToLight[i] = lightPoses[i] - input.position;
	}
	return output;
}
//--------------------------------------------------------------------------------
 
//main pixel program
//--------------------------------------------------------------------------------
float4 multiTypeLightPS(	vertexOut 	input,
			uniform float4		SLParamsArray[lightCount],
			uniform float3		lightDirs[lightCount],
			uniform	float4		diffColors[lightCount],
			uniform	float4 		specColors[lightCount],
			uniform float4		lightAttens[lightCount],
			uniform float4		lightDists[lightCount],
			uniform	float4		ambientColor,
			uniform float		specShine
			) : COLOR
{
	float4 diff 	= float4(0, 0, 0, 0);
	float4 spec 	= float4(0, 0, 0, 0);
	
	input.viewDir	= normalize( input.viewDir );
	input.normal 	= normalize( input.normal );
	
	for(int i = 0; i<lightCount ; i++)
	{
		input.pixelToLight[i]	= normalize( input.pixelToLight[i] );
		
		light(	input.normal, 
			input.viewDir, 
			input.pixelToLight[i],
			normalize(lightDirs[i]),
			SLParamsArray[i],
			diffColors[i],
			specColors[i],
			lightAttens[i],
			lightDists[i],
			specShine,
			diff,
			spec);
	}
	return ambientColor + diff + spec ;
}
//--------------------------------------------------------------------------------


The shader in action; red directional, blue point light from below and white spotlight from the left.
Image

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