Dot product is a cheap and useful function in many situations. It calculate the cosAngle to two unit vectors which is 1 when acute, 0 to -1 for obtuse angle. These are some applications which I found very useful.
Check if two unit are facing each other by dot product their forwardVec, for 3D you can optionally ignore the height component for the vectors.
For airplane game, prevent a plane from over pitching by checking the planeDir dot worldUpVec and worldDownVec.
Test if an unit has passed a waypoint, assuming the unit is moving forward. Do a distance check to ensure the unit is near the waypoint. do a dot product between the unit forward vector and the direction to the waypoint, if the angle is obtuse, mean the unit has pass the waypoint.
For terrain dot product normals of two face to find out the steepness of a slope.
NdotL for lambert diffuse
NdotH for blinn specular
RdotV for phong specular
NdotV to detect edges of the model.
Using a keyboard buffer for intuitive user inputs
Code length: Short
_lastActions is the latest player action.
_lastAction is the action buffer.
if(e.key == keyMap[PLAYER_MOVE_UP])
_lastActions = _lastActions;
_lastActions = PLAYER_MOVE_UP;
//player move up
In any case got to reset the action buffer.
if(_lastActions == PLAYER_MOVE_UP)
_lastActions = _lastKeys;
//process the previous player action.
_lastActions = PLAYER_NOT_MOVING;
else if(_lastActions == PLAYER_MOVE_UP)
_lastActions = PLAYER_NOT_MOVING;
PLAYER_NOT_MOVING = 0,
Not A Number
NaN is an insidious bug that often plague games and shader programs during development. If you are lucky, you would probably never encounter it before, but the first time would often be very painful.
It begin with a single unit disappearing from the map, then suddenly whole armies are teleported somewhere, and at last the player is teleported to limbo.
On a shader program, it is less obvious, as the color of NaN is BLACK!!! So for most of the time it would seem just like a few black speck on the screen. But turning on effect like HDR when there is a NaN would cause the whole screen to blacken out.
The worst thing about NaN is, it is more contagious than the plague. Any maths operator with a NaN would give you a NaN
Luckily there are not many ways to cause NaN. The most common ways and solution are
Division by zero
Have a check to ensure your divisor is not zero. In certain situations with a positive divisor, we can add a very small number to the divisor to ensure it is not zero.
Normalize a zero vector
Remember to normalize a vector is to divide every component of a vector with it magnitude. So to normalize a zero vector would cause a divison by zero. Do a check on the vector length or lengthSquare to ensure it is not zero before normalizing it.
Zero vector Normals are also very common in exported model, it could be the normal is not exported or some bug with teh exported, to export a zero normal. I often find a shader to display normals as color to be useful in such situation. If you have control over the content pipeline, Assert when there is a zero normal.
Calling ACos on a number outside -1 to 1
Dot product of two unit vectors would give the cosAngle. if any of the two vectors is not unit length, the result would probably be outside -1 to 1. Ensure both vectors are unit length, and try not to call ACos as cosAngle is very sufficent to solve most problems.
It would commonly take in 3 scaler or 2 vector and a scaler, and return the result of the formula
x + s(y-x).
I often find this function useful for cheap generation of points along a relatively straight line. It is also very useful to calculate the display of health/power/magic bar, eg
healthBarLength = lerp(healthBarStart, healthBarMaxLength, %healthLeft)
In UI it is a very good helper function to convert relative screencoord to absolute screencoord
It is frequently used for alpha blending, blending of normal maps, terrain splatting. I like to use it for signal scaling,
eg getting value max(0, NdotL) / max(0, NdotV) to scale to some other values for various effects.
Boost Bind imo is one of the most useful library in C++, yet at times can be the most frustrating one too!
For the uninitiate
This is a small example on the usefulness of boost bind. We have a FunctionClass which that in a function, and will execute the function sometime later. I will not go into detail on why the function will be executed later, below is the class.
typedef boost::function Callback;
FunctionClass (const Callback & callback) :
virtual void executeCallback()
Now the class will only take in a function that take in no parameters and return no parameters. If we writing our own function, we can still ensure it work with the Callback. Let say we need to call a function from a third pty library.
Eg. SceneNode::setPosition at Vector3(0, 0, 0);
We could always create a helper function
What happen if we need to call setPosition at multiple differnt location???
This is where boost bind come to the rescue!!!
Callback myCallback = boost
bind(&SceneNode::setPosition, myNode, Vector3(0, 0, 0));
A simple one line of code to fufill our needs!!!
…. more examples to follow
I am using HLSL shader model 3, but this article should apply to other languages and shader models.
It is Good to MAD
One of the most basic optimisation is to use mad operation, which is to multiply 2 values and add a third value to the result.
This is two instructions for the price of one, luckily the compiler is usually smart enough to snap this bargain when they sense it.
It is still useful to look at the compiled asm to combine any exceptions
The Power of 4
The beauty of GPU is most instructions are process in 4 components data block. This will caused any instruction that uses 1 data to cost as much as the same instruction using 4 data.
Eg pow(NdotH, shininess) cost the same as pow(float4(light1NdotH, light2NdotH, light3NdotH, light4NdotH), shininess)
Step operation and comparision operator also work in 4
float4 results = step(sampleDepths, depthToCompare);
float4 results = (sampleDepths > depthToCompare);
When 4 become 1
After comparision, it is often desirable to combine the results together to get total number of samples compared correctly.
This is where dotproduct shine.
Remember dot product of 2 float4 is
vec1.x * vec2.x + vec1.y * vec2.y + vec1.z * vec2.z + vec1.w * vec2.w
which is 4 mad instruction for 1 dp4 instruction
float numberOfResultsTrue = dot(results, 1);
Cheap Matrix Inverse
Remember orthonormal matrices Inverse is equal to their Transpose. Tangent, Binormal(Bitangent), Normal are usually in unit length and are perpendicular to each other. Use their transpose to convert any tangent space vector back to object space.
float3x3 matTan = float3x3(T, B, N);
float3x3 matTanInverse = transpose(matTan);
float3 worldNormal = mul(matTanInverse, normalFromNormalMap);
RenderMonkey has a very Cool Texture generator, that allow you to generate a texture from HLSL.
Well It is cool until you need to generate a random texture from UV.
Here are some quick code that is prob not mathematically correct, but it work for me.
float4 Texture2DFill( float2 vTexCoord : POSITION,
float2 vTexelSize : PSIZE) : COLOR
float uvFactor = dot(vTexCoord, float2( 1528.4f, 51.3f));
float rand = frac(fmod(uvFactor * 51223.00445, 20)) * 20;
rand *= uvFactor;
rand *= sqrt(rand * 347);
rand = fmod(rand, 2 * 3.1412 * uvFactor);
rand = frac(rand);
Combining tangent space normal map is different from combining normal images. Here are some ways to combine two normal map together. The general idea is the identity normal, float3(0, 0, 1), will use the vertex default normal.
Adding two normals and preserving both details can be done this way.
finalNormal = float3(normal1.xy + normal2.xy, normal1.z * normal2.z);
finalNormal = normalize(finalNormal);
Using lerp. we can easily blend two normal
lerp(normal1, normal2, factor)
To make the normal map look stronger we could do
normal.xy *= strength;
This will cause any slope to bent away from the surface normal making it look steeper.
To compress normal, it is common to copy the X value to the A channel of the image, and calculate the Z value from X and Y
In short it is to take advantage of the uncompressed A channel in DXT5 and to save an additional channel data by calculating Z during runtime.
normal.xy = tex2D(normalMap, uv).ag;
normal.z = sqrt(1 – normal.x * normal.x – normal.y * normal.y);
which can be optimise to
normal.z = sqrt(1 – dot(normal.xy, normal.xy));
A Power function raised x to specific power.
It has an interesting property when x is between 0 – 1, the result will be always between 0 – 1. Do take note Power function will not preserve the sign of x, it may be necessary to calculate the sign beforehand.
What Power does is to change the curve of x to favor certain values.
This is the curve for using a joystick to aim at something. Typically when gamers want to have a fast movement on analog stick, They would push the analog stick to max. Using the Power function we can allocate 80% of the analog controls to slower movement, so gamers would have more control over aiming, yet allow the quick movement by pushing the analog stick to max.
Power is also very commonly used in graphics, We could use it to change color curves, contrast of images, fade off of lighting equation/fog/glows and many more.