I did make algorithm for creating Bézier Curve with Objective-C and Cocos2D. Here is my code
-(int)factorial:(int)x{
int sum=1;
int i;
if(x == 0){
return 1;
}else{
for(i=1;i<x;i++){
sum = sum*i;
}
return sum;
}
}
-(int)binomialCoefficient:(int)n:(int)i{
int sum;
//NSLog([NSString stringWithFormat:#"fac n-i=%f\n", fach] );
sum = [self factorial:n]/([self factorial:i]*[self factorial:(n-i)]);
return sum;
}
-(float)convertT:(int)t{
return t*(0.001);
}
-(float)power:(float)a:(int)b{
int i;
float hasil=1;
for(i=0;i<b;i++){
hasil = hasil*a;
}
return hasil;
}
-(float)bernstein:(float)t:(int)n:(int)i{
float sum = 0;
sum = [self binomialCoefficient:n:i]*[self power:t :i]*[self power:(1-t) :(n-i)];
//NSLog([NSString stringWithFormat:#"yeah"]);
return sum;
}
and for implementation you just put an array of x and y and access it. For example to draw a single dot in control curve I did it like this
float myPx = px[i];
float myPy = py[i];
posx = posx+([self bernstein:theT :banyak-1 :i]*myPx);
posy = posy+([self bernstein:theT :banyak-1 :i]*myPy);
Yes, this code doesn't give the perfect nice line, but I try to draw it dot by dot.
It works well, but the problem arise when I try to use 3 dots. The middle dot for curving the lines didn't behave like what I expected. For example if I put 3 dots in these coordinates:
a(100,200)
b(250,250)
c(500,200)
It didn't curving up but curving down. If I want to put it straight I have to put it all the way higher.
Am I do it wrong in syntax or data types? Or is it just my algorithm?
Thanks in advance
Best Regards
(sorry for my bad english)
The factorial loop should be
for ( i = 1 ; i <= x ; i++ )
instead of
for ( i = 1 ; i < x ; i++ )
Related
i'm trying to make this interaction with keyboard for movement using some sprites and i got stuck with two situations.
1) The character movement is not going acording to the animation itself (it only begin moving after one second or so while it's already being animated). What i really want it to do is, to move without a "initial acceleration feeling" that i get because of this problem
2) I can't think of a way to make the character face the position it should be facing when the key is released. I'll post the code here, but since it need images to work correctly and is not so small i made a skecth available at this link if you want to check it out: https://www.openprocessing.org/sketch/439572
PImage[] reverseRun = new PImage [16];
PImage[] zeroArray = new PImage [16];
void setup(){
size(800,600);
//Right Facing
for(int i = 0; i < zeroArray.length; i++){
zeroArray[i] = loadImage (i + ".png");
zeroArray[i].resize(155,155);
}
//Left Facing
for( int z = 0; z < reverseRun.length; z++){
reverseRun[z] = loadImage ( "mirror" + z + ".png");
reverseRun[z].resize(155,155);
}
}
void draw(){
frameRate(15);
background(255);
imageMode(CENTER);
if(x > width+10){
x = 0;
} else if (x < - 10){
x = width;}
if (i >= zeroArray.length){
i = 3;} //looping to generate constant motiion
if ( z >= reverseRun.length){
z = 3;} //looping to generate constant motiion
if (isRight) {
image(zeroArray[i], x, 300);
i++;
} //going through the images at the array
else if (isLeft) {
image(reverseRun[z],x,300);
z++;
} going through the images at the array
else if(!isRight){
image(zeroArray[i], x, 300);
i = 0; } //"stoped" sprite
}
}
//movement
float x = 300;
float y = 300;
float i = 0;
float z = 0;
float speed = 25;
boolean isLeft, isRight, isUp, isDown;
void keyPressed() {
setMove(keyCode, true);
if (isLeft ){
x -= speed;
}
if(isRight){
x += speed;
}
}
void keyReleased() {
setMove(keyCode, false);
}
boolean setMove(int k, boolean b) {
switch (k) {
case UP:
return isUp = b;
case DOWN:
return isDown = b;
case LEFT:
return isLeft = b;
case RIGHT:
return isRight = b;
default:
return b; }
}
The movement problem is caused by your operating system setting a delay between key presses. Try this out by going to a text editor and holding down a key. You'll notice that a character shows up immediately, followed by a delay, followed by the character repeating until you release the key.
That delay is also happening between calls to the keyPressed() function. And since you're moving the character (by modifying the x variable) inside the keyPressed() function, you're seeing a delay in the movement.
The solution to this problem is to check which key is pressed instead of relying solely on the keyPressed() function. You could use the keyCode variable inside the draw() function, or you could keep track of which key is pressed using a set of boolean variables.
Note that you're actually already doing that with the isLeft and isRight variables. But you're only checking them in the keyPressed() function, which defeats the purpose of them because of the problem I outlined above.
In other words, move this block from the keyPressed() function so it's inside the draw() function instead:
if (isLeft ){
x -= speed;
}
if(isRight){
x += speed;
}
As for knowing which way to face when the character is not moving, you could do that using another boolean value that keeps track of which direction you're facing.
Side note: you should really try to properly indent your code, as right now it's pretty hard to read.
Shameless self-promotion: I wrote a tutorial on user input in Processing available here.
I'm making a bidirectional path tracer and I have some troubles.
To be clear :
1) One point light
2) All objects are diffuse
3) All objects are spheres, even walls (they are very large)
4) NO MIS WEIGHTING
The light emission is a 3D vector. The BRDF of a sphere is a 3D vector. Hard coded.
In the main function below I generate EyePath and LightPath then I connect them. At least I try.
In this post I will talking about the main function then EyePath then LightPath. The talking about connecting function will appear once EyePath and Light are good.
First questions :
Does the generation of the first light point is good ?
Do I need to compute this point according to the emission of the light source? or is it just the emission ? The line is commented where i'm filling the Vertices structure.
Do I need to translate fromlight ? In order to put it on the sphere
The code below is sampled in the main function. Above it there is two for loops going through all pixels. Camera.o is the eye. CameraRayDir is the direction to the current pixel.
//The path light starting point is at the same position as the light
Ray fromLight(Vec(0, 24.3, 0), Vec());
Sphere light = spheres[7];
#define PDF 0.15915494309 // 1 / (2 * PI)
for(int i = 0; i < samps; ++i)
{
std::vector<Vertices> PathEye;
std::vector<Vertices> PathLight;
Vec cameraRayDir = cx * (double(x) / w - .5) + cy * (double(y) / h - .5) + camera.d;
Ray rayEye(camera.o, cameraRayDir.norm());
// Hemisphere oriented towards the top
fromLight.d = generateRayInHemisphere(fromLight.o,Vec(0,1,0)).d;
double f = clamp(n.dot(fromLight.d.norm()));
Vertices vert;
vert.d = fromLight.d;
vert.x = fromLight.o;
vert.id = 7;
vert.cos = f;
vert.n = Vec(0,1,0).norm();
// this one ?
//vert.couleur = spheres[7].e * f / PDF;
// Or this one ?
vert.couleur = spheres[7].e;
PathLight.push_back(vert);
int sizeEye = generateEyePath(PathEye, rayEye, maxDepth);
int sizeLight = generateLightPath(PathLight, fromLight, maxDepth);
for (int s = 0; s < sizeLight; ++s)
{
for (int t = 1; t < sizeEye; ++t)
{
int depth = t + s - 1;
if ((s == 0 && t == 0) || depth < 0 || depth > maxDepth)
continue;
pixelValue = pixelValue + connectPaths(PathEye, PathLight, s, t);
}
}
}
For the EyePath I intersect the geometry then I compute the illumination according to the distance with the light. The colour is black if the point is in the shadow.
Second question : For the eye path and the direct illumination, is the computation good ? I've seen in many code, people use the pdf even in direct illumination. But I'm only using point light and spheres.
int generateEyePath(std::vector<Vertices>& v, Ray eye, int maxDepth)
{
double t;
int id = 0;
Vertices vert;
int RussianRoulette;
while(v.size() <= maxDepth)
{
if(distribRREye(generatorRREye) < 10)
break;
// Intersect all the geometry
// id is the id of the intersected geometry in an array
intersect(eye, t, id);
const Sphere& obj = spheres[id];
// Intersection point
Vec x = eye.o + eye.d * t;
// normal
Vec n = (x - obj.p).norm();
Vec direction = light.p - x;
// Shadow ray
Ray RaytoLight = Ray(x, direction.norm());
const float distance = direction.length();
// shadow
const bool visibility = intersect(RaytoLight, t, id);
const Sphere &lumiere = spheres[id];
float degree = clamp(n.dot((lumiere.p - x).norm()));
// If the intersected geometry is not a light, then in shadow
if(lumiere.e.x == 0)
{
vert.couleur = Vec();
}
else // else we compute the colour
// obj.c is the brdf, lumiere.e is the emission
vert.couleur = (obj.c).mult(lumiere.e / (distance * distance)) * degree;
vert.x = x;
vert.id = id;
vert.n = n;
vert.d = eye.d.normn();
vert.cos = degree;
v.push_back(vert);
eye = generateRayInHemisphere(x,n);
}
return v.size();
}
For the LightPath, for a given point, I compute it according to the previous one and the values at this point. Like in a common path tracing.\n
Third question: Is the colour computation good ?
int generateLightPath(std::vector<Vertices>& v, Ray fromLight, int maxDepth)
{
double t;
int id = 0;
Vertices vert;
Vec previous;
while(v.size() <= maxDepth)
{
if(distribRRLight(generatorRRLight) < 10)
break;
previous = v.back().couleur;
intersect(fromLight, t, id);
// intersected geometry
const Sphere& obj = spheres[id];
// Intersection point
Vec x = fromLight.o + fromLight.d * t;
// normal
Vec n = (x - obj.p).norm();
double f = clamp(n.dot(fromLight.d.norm()));
// obj.c is the brdf
vert.couleur = previous.mult(((obj.c / M_PI) * f) / PDF);
vert.x = x;
vert.id = id;
vert.n = n;
vert.d = fromLight.d.norm();
vert.cos = f;
v.push_back(vert);
fromLight = generateRayInHemisphere(x,n);
}
return v.size();
}
For the moment I get this result.
enter image description here
The connecting function will come once EyePath and LightPath are good.
Thank you all
Try the spherical reference scene mentioned in this paper. I think then you can work out most of your questions by yourself since it has an analytical solution.
https://www.researchgate.net/publication/221546261_Testing_Monte-Carlo_Global_Illumination_Methods_with_Analytically_Computable_Scenes
It would save your time to implement and verify your understanding with path tracing and light tracing first, then try to combine them with weights.
Hi so I am trying to create an if statement where...if the sprite has been touched...then something will happen
However, for some reason, I am getting an expected identified error and can't for the life of me figure out why?
Thank you for any help and knowledge you can provide meKKInput* input = [KKInput sharedInput];
KKInput* input = [KKInput sharedInput];
if([input isAnyTouchOnNode:kan touchPhase:[KKTouchPhaseAny]])
{
for ( int x = 105.0f; x < 100000 ; ++x)
{
for ( int y = 50.0f; y < 100000 ; ++y)
{
kan.position = CGPointMake((x),(y));
}
}
}
The square brackets around KKTouchPhaseAny (probably an enum) must be removed.
I have to multiply 2 large integer numbers, every one is 80+ digits.
What is the general approach for such kind of tasks?
You will have to use a large integer library. There are some open source ones listed on Wikipedia's Arbitrary Precision arithmetic page here
We forget how awesome it is that CPUs can multiply numbers that fit into a single register. Once you try to multiply two numbers that are bigger than a register you realize what a pain in the ass it is to actually multiply numbers.
I had to write a large number class awhile back. Here is the code for my multiply function. KxVector is just an array of 32 bit values with a count, and pretty self explanatory, and not included here. I removed all the other math functions for brevity. All the math operations are easy to implement except multiply and divide.
#define BIGNUM_NEGATIVE 0x80000000
class BigNum
{
public:
void mult( const BigNum& b );
KxVector<u32> mData;
s32 mFlags;
};
void BigNum::mult( const BigNum& b )
{
// special handling for multiply by zero
if ( b.isZero() )
{
mData.clear();
mFlags = 0;
return;
}
// apply sign
mFlags ^= b.mFlags & BIGNUM_NEGATIVE;
// multiply two numbers using a naive multiplication algorithm.
// this would be faster with karatsuba or FFT based multiplication
const BigNum* ppa;
const BigNum* ppb;
if ( mData.size() >= b.mData.size() )
{
ppa = this;
ppb = &b;
} else {
ppa = &b;
ppb = this;
}
assert( ppa->mData.size() >= ppb->mData.size() );
u32 aSize = ppa->mData.size();
u32 bSize = ppb->mData.size();
BigNum tmp;
for ( u32 i = 0; i < aSize + bSize; i++ )
tmp.mData.insert( 0 );
const u32* pb = ppb->mData.data();
u32 carry = 0;
for ( u32 i = 0; i < bSize; i++ )
{
u64 mult = *(pb++);
if ( mult )
{
carry = 0;
const u32* pa = ppa->mData.data();
u32* pd = tmp.mData.data() + i;
for ( u32 j = 0; j < aSize; j++ )
{
u64 prod = ( mult * *(pa++)) + *pd + carry;
*(pd++) = u32(prod);
carry = u32( prod >> 32 );
}
*pd = u32(carry);
}
}
// remove leading zeroes
while ( tmp.mData.size() && !tmp.mData.last() ) tmp.mData.pop();
mData.swap( tmp.mData );
}
It depends on what you want to do with the numbers. Do you want to use more arithmetic operators or do you simply want to multiply two numbers and then output them to a file? If it's the latter it's fairly simple to put the digits in an int or char array and then implement a multiplication function which works just like you learned to do multiplication by hands.
This is the simplest solution if you want to do this in C, but of course it's not very memory efficient. I suggest looking for Biginteger libraries for C++, e.g. if you want to do more, or just implement it by yourself to suit your needs.
I am trying to increase the performance of the update(); function below. The numbers inside the mathNumber variable will come from an NSString created from a text field. Even though I'm using five numbers I would like it to be able to run any amount that the user inserts into a text field. What are some ways I could speed up the code in update(); with C and/or Objective-C? I also would like it to work on the Mac and iPhone.
typedef struct {
float *left;
float *right;
float *equals;
int operation;
} MathVariable;
#define MULTIPLY 1
#define DIVIDE 2
#define ADD 3
#define SUBTRACT 4
MathVariable *mathVariable;
float *mathPointer;
float newNumber;
void init();
void update();
float solution(float *left, float *right, int *operation);
void init()
{
float *mathNumber = (float *) malloc(sizeof(float) * 9);
mathNumber[0] =-1.0;
mathNumber[1] =-2.0;
mathNumber[2] = 3.0;
mathNumber[3] = 4.0;
mathNumber[4] = 5.0;
mathNumber[5] = 0.0;
mathNumber[6] = 0.0;
mathNumber[7] = 0.0;
mathNumber[8] = 0.0;
mathVariable = (MathVariable *) malloc(sizeof(MathVariable) * 4);
mathVariable[0].equals = &mathPointer[5];
mathVariable[0].left = &mathPointer[2];
mathVariable[0].operation = MULTIPLY;
mathVariable[0].right = &mathPointer[3];
mathVariable[1].equals = &mathPointer[6];
mathVariable[1].left = &mathPointer[1];
mathVariable[1].operation = SUBTRACT;
mathVariable[1].right = &mathPointer[5];
mathVariable[2].equals = &mathPointer[7];
mathVariable[2].left = &mathPointer[0];
mathVariable[2].operation = ADD;
mathVariable[2].right = &mathPointer[6];
mathVariable[3].equals = &mathPointer[8];
mathVariable[3].left = &mathPointer[7];
mathVariable[3].operation = MULTIPLY;
mathVariable[3].right = &mathPointer[4];
return self;
}
// This is updated with a timer
void update()
{
int i;
for (i = 0; i < 4; i++)
{
*mathVariable[i].equals = solution(mathVariable[i].left, mathVariable[i].right, &mathVariable[i].operation);
}
// Below is the equivalent of: newNumber = (-1.0 + (-2.0 - 3.0 * 4.0)) * 5.0;
// newNumber should equal -75
newNumber = mathPointer[8];
}
float solution(float *left, float *right, int *operation)
{
if ((*operation) == MULTIPLY)
{
return (*left) * (*right);
}
else if ((*operation) == DIVIDE)
{
return (*left) / (*right);
}
else if ((*operation) == ADD)
{
return (*left) + (*right);
}
else if ((*operation) == SUBTRACT)
{
return (*left) - (*right);
}
else
{
return 0.0;
}
}
EDIT:
I first must say thank you for all of your kind posts. This is the first forum I've gotten people that don't tell me I'm a complete idiot. Sorry about the return self; I didn't realize this was an objective-C forum too (thus why I hastily used C). I have my own parser which is slow but I'm not concerned with its speed. All I want is to speed up the update() function since it slows everything down and 90% of the objects use it. Also, I'm try to get it to work faster with iOS devices since I can't compile anything in the text boxes. If you have any other advice on making update() faster I thank you.
Thanks again,
Jonathan
EDIT 2:
Well I got it to run faster by changing it from:
int i;
for (i = 0; i < 4; i++)
{
*mathVariable[i].equals = solution(*mathVariable[i].left, *mathVariable[i].right, mathVariable[i].operation);
}
To:
*mathVariable[0].equals = solution(*mathVariable[0].left, *mathVariable[0].right, mathVariable[0].operation);
*mathVariable[1].equals = solution(*mathVariable[1].left, *mathVariable[1].right, mathVariable[1].operation);
*mathVariable[2].equals = solution(*mathVariable[2].left, *mathVariable[2].right, mathVariable[2].operation);
*mathVariable[3].equals = solution(*mathVariable[3].left, *mathVariable[3].right, mathVariable[3].operation);
Is there any other way to increment it as fast as the preloaded numbers in the array like above?
Your code is a mix of styles, and contains some unwarranted uses of pointers (e.g. when passing operation to solution). It is unclear why you are passing the floats by reference, but maybe you intend that these change be changed and the expression reevaluated?
Below are some changes both to tidy and incidentally speed it up - the cost of any of this is not high and you may be guilt of premature optimization. As #Dave commented there are libraries to do parsing for you, but if you're targeting simple math expressions an operator precedence stack-based parser/evaluator is easy enough to code.
Suggestion 1: use enum - cleaner:
typedef enum { MULTIPLY, DIVIDE, ADD, SUBTRACT } BinaryOp;
typedef struct
{
float *left;
float *right;
float *equals;
BinaryOp operation;
} MathVariable;
Suggestion 2: use switch - cleaner and probably faster as well:
float solution(float left, float right, int operation)
{
switch(operation)
{
case MULTIPLY:
return left * right;
case DIVIDE:
return left / right;
case ADD:
return left + right;
case SUBTRACT:
return left - right;
default:
return 0.0;
}
}
Note I also removed passing pointers, the call is now:
*mathVariable[i].equals = solution(*mathVariable[i].left,
*mathVariable[i].right,
mathVariable[i].operation);
Now an OO person will probably object (:-)) to the switch (or the if/else) and argue each node (your MathVariable) should be an instance which knows how to perform its own operation. A C person might suggest you use function pointers in the node so they can perform their own operation. All this is design and you'll have to figure that out yourself.