I want to preface this post: This is perhaps more of a math question than a coding question.
I am developing a plant (lettuce) model which involves somewhat complex geometry. At this stage I have a surface curved in 2 dimensions but now I want to add waviness to this curved surface but am having a hard time envisioning how to do so. The surface is made of triangle primatives, the primatives take xyz vectors to encode location of vertices. I am using an API termed HELIOS to develop this procedural model of lettuce. I essentially created the surface with for loops and the sine function. Disclaimer: I do not have a strong background in geometry, computer graphics, or C++.
Here is the relevant code:
#include "Context.h"
#include "Visualizer.h"
using namespace helios;
using namespace std;
vector<uint> addLeaf(float leaf_length, float leaf_width, float leaf_bend_x, float leaf_bend_y, float rotation_z, float rotation_x, float displacement, float radius, Context* context ) {
std::vector<uint> UUIDs;
// float leaf_length = 10;
float Nz = 10; // params.s1_leaf_subdivisions ; number of times to split the dimension
float dz = leaf_length / Nz; // length of each subdivision
// float leaf_width = 10;
float Ny = 10; // params.s1_leaf_subdivisions ; number of times to split the dimension
float dy = leaf_width / Ny; // length of each subdivision
// leaf wave
// float A_3 = leaf_length * float(0.5); // Half waves on the leaf 10
// float A_2 = leaf_length * float(0.1); // amplitude 0.25
float A_3 = 1; // Half waves on the leaf 10
float A_2 = 1; // amplitude 0.25
float leaf_amplitude = leaf_length / float(10);
// the 2 * dx extends the sine wave a bit beyond 1/2 wavelength so base of leaves come together
for (int i = 0; i < Nz + (2 * dz); i++) {
for (float j = 0; j < Ny; j++) {
float z = i * dz; //for each subdivision in z define Z coord
float y = j * dy; //for each subdivision in y define y coord
float x = 0; // we will also need an x coord
float sz = dz; // the next step in z will be equal to a subdivision in z
float sy = dy; // the next step in y will be equal to a subdivision in y
float z_i = z * M_PI / (Nz * dz); // the second coord for z is z_i needed to define a triangle primitive
float sz_i = (z + sz) * M_PI / (Nz * dz); //
// this would be y_1 in sorghum model
float y_i = (y * M_PI / (Ny * dy)) / (A_3); // the second coord for y is y_i needed to define a triangle primitive
float sy_i = ((y + sy) * M_PI / (Ny * dy)) / (A_3);
//waviness of leaf
float leaf_wave_1;
float leaf_wave_2;
float leaf_wave_3;
float leaf_wave_4;
if (j == 0) {
leaf_wave_1 = A_2 * sin(z_i);
leaf_wave_2 = A_2 * sin(sz_i);
} else {
leaf_wave_1 = A_2 * sin(z_i);
leaf_wave_2 = A_2 * sin(sz_i);
}
// Now define x based on z,y and add leaf bend in x and y
x = leaf_bend_x * sin(z_i);
x = ((x*radius + displacement + (leaf_bend_y * sin(y_i))) / 2) + leaf_wave_1;
vec3 v0(x*radius + displacement, y, z);
x = leaf_bend_x * sin(sz_i);
x = ((x*radius + displacement + (leaf_bend_y * sin(y_i))) / 2) + leaf_wave_2;
vec3 v1(x*radius + displacement, y, z + sz);
if (j == Nz - 1) {
leaf_wave_3 = sin(sz_i) * A_2;
leaf_wave_4 = sin(z_i) * A_2;
} else {
leaf_wave_3 = sin(sz_i) * A_2;
leaf_wave_4 = sin(z_i) * A_2;
}
x = leaf_bend_x * sin(sz_i);
x = ((x*radius + displacement + (leaf_bend_y * sin(sy_i))) / 2) + leaf_wave_3 ;
vec3 v2(x*radius + displacement, y + sy, z + sz);
x = leaf_bend_x * sin(z_i);
x = ((x*radius + displacement + (leaf_bend_y * sin(sy_i))) / 2) + leaf_wave_4 ;
vec3 v3(x*radius + displacement, y + sy, z);
// set of two triangles which form a rectangle or square as subunits of leaf
UUIDs.push_back(context->addTriangle(v0, v1, v2, RGB::cyan));
UUIDs.push_back(context->addTriangle(v0, v2, v3, RGB::magenta));
}
}
return UUIDs;
}
// call to functions and build lettuce geometries
int main( void ){
Context context;
float leaf_length = 10;
float leaf_width = 10;
float radius = 1; // additional control leaf curvature
// add leaves one by one; 'i' here is # of leaves external to whorl
for (int i = 0; i < 6; i++) {
if (i == 0)addLeaf(leaf_length, leaf_width, 0.5*leaf_length, 0.5*leaf_width, 4 * M_PI / 9*i, 0, i/5, radius, &context);
// if (i == 1)addLeaf(leaf_length, leaf_width, 0.5*leaf_length, 0.5*leaf_width, 4 * M_PI / 9*i, -M_PI/ 20, i/5, radius, &context);
// if (i == 2)addLeaf(leaf_length, leaf_width, 0.5*leaf_length, 0.5*leaf_width, 4 * M_PI / 9*i, -M_PI/ 10, i/5, radius, &context);
// if (i == 3)addLeaf(leaf_length, leaf_width, 0.5*leaf_length, 0.5*leaf_width, 4 * M_PI / 9*i, -M_PI/ 9, i/5, radius, &context);
// if (i == 4)addLeaf(leaf_length, leaf_width, 0.5*leaf_length, 0.5*leaf_width, 4 * M_PI / 9*i, -M_PI/ 7, i/5, radius, &context);
// if (i == 5)addLeaf(leaf_length, leaf_width, 0.5*leaf_length, 0.5*leaf_width, 4 * M_PI / 9*i, -M_PI/ 5, i/5, radius, &context);
}
Visualizer visualizer(800);
visualizer.buildContextGeometry(&context);
visualizer.setLightingModel(Visualizer::LIGHTING_PHONG);
visualizer.plotInteractive();
}
I tried to use a sine function and an additional for loop to create a series of values to add to the X coordinate of the triangles but did not obtain the result I was looking for.
This is how you can create a Wave Geometry.
you can keep updating the m_fTime values to animate the wave.
// m_iWaveFlowOut -> value to be either 0 or 1
//m_fFrequency -> Number of waves
//m_fAmplitude -> Amplitude of wave
void Generate()
{
const int n8 = m_iNSegments * 8; // size of VBO gfx data
const int sz0 = m_iMSegments * n8; // size of VBO gfx data
const int sz1 = (m_iMSegments - 1) * (m_iNSegments - 1) * 6;// size of indices
verticesRect.clear();
indicesRect.clear();
int a,i, j, k, b;
float x, y, z, dx, dy, l;
glm::vec3 u, v, nor;
dx = 2.0 * ( m_fWidth / float(m_iNSegments - 1));
dy = 2.0 * ( m_fHeight / float(m_iMSegments - 1));
for (a = 0, y = -m_fHeight, j = 0; j < m_iMSegments; j++, y += dy)
for (x = -m_fWidth, i = 0; i < m_iNSegments; i++, x += dx)
{
float dist = glm::length(glm::vec2(x + m_fxOffset, y + m_fyOffset));
float attenuation, kc, kq;
kc = 1.0; kq = 0.0;
attenuation = 1.0f;
if (m_bUseAttenuation) {
attenuation = 1.0 / (kc + (this->m_fKl * dist) + (kq * pow(dist, 2)));
if (attenuation > 1.0) attenuation = 1.0;
}
switch (m_WAVETYPE)
{
case Sum_Wave2::WAVE2_TYPE::COS:
z = (-m_fAmplitude * attenuation) * cos(((x + m_fxOffset) / m_fFrequency) + m_fTime * m_iWaveFlowOut);
break;
case Sum_Wave2::WAVE2_TYPE::SIN:
z = (-m_fAmplitude * attenuation) * sin(((y + m_fyOffset) / m_fFrequency) + m_fTime * m_iWaveFlowOut);
break;
case Sum_Wave2::WAVE2_TYPE::RING:
z = (-m_fAmplitude * attenuation) * sin((glm::length(glm::vec2(x + m_fxOffset, y + m_fyOffset)) + m_fTime * m_iWaveFlowOut) / m_fFrequency);
break;
default:
z = 0.0;
break;
}
verticesRect.push_back(x); a++;
verticesRect.push_back(y); a++;
verticesRect.push_back(z); a++;
// Normal ( will be recomputed later)
verticesRect.push_back(0.0); a++;
verticesRect.push_back(0.0); a++;
verticesRect.push_back(1.0); a++;
// TexCoord
verticesRect.push_back((x + m_fWidth) / (m_fWidth + m_fWidth)); a++;
verticesRect.push_back((y + m_fHeight) / (m_fHeight + m_fHeight)); a++;
}
// triangulation indices
for(a = 0, j = 1; j < m_iMSegments; j++ )
for (i = 1; i < m_iNSegments; i++)
{
b = ((m_iNSegments * j) + i) * 8;
// First triangle per quad
indicesRect.push_back(b - 8); a++;
indicesRect.push_back(b - 8 - n8); a++;
indicesRect.push_back(b); a++;
// Second triangle per quad
indicesRect.push_back(b - 8 - n8); a++;
indicesRect.push_back(b - n8); a++;
indicesRect.push_back(b); a++;
// recompute inner normals
for (k = 0; k < 3; k++) {
u[k] = verticesRect[indicesRect[a - 6] + k] - verticesRect[indicesRect[a - 4] + k];
v[k] = verticesRect[indicesRect[a - 5] + k] - verticesRect[indicesRect[a - 4] + k];
}
glm::vec3 cross1 = crossProduct(u, v);
cross1 = glm::normalize(cross1);
for (k = 0; k < 3; k++) {
u[k] = verticesRect[indicesRect[a - 3] + k] - verticesRect[indicesRect[a - 1] + k];
v[k] = verticesRect[indicesRect[a - 2] + k] - verticesRect[indicesRect[a - 1] + k];
}
glm::vec3 cross2 = crossProduct(u, v);
cross2 = glm::normalize(cross2);
for (k = 0; k < 3; k++) {
verticesRect[indicesRect[a - 1] + 3 + k] = 0.5 * (cross1[k] + cross2[k]);
}
}
for (i = 0; i < sz1; i++) {
indicesRect[i] = indicesRect[i] /= 8;
}
}
I'm trying to implement spline Catmull-Rom for image zooming using C++ and OpenCV.
I performed two tests, the first is image zooming (X2), and the second image reconstruction (zooming image decimated).
My problem is that in the image interpolated appear some white and black pixel (image1) when I displayed the value of pixels I found that white pixels have a negative value and the black one has a value greater than 255, also the image reconstructed appear blurred (image2 and image3).
float CalCurveInt(float t, float p0, float p1, float p2, float p3)
{
float t2 = t * t;
float t3 = t2 * t;
float x = 0.5f * ((2.0f * p1) +
(-p0 + p2) * t +
(2.0f * p0 - 5.0f * p1 + 4 * p2 - p3) * t2 +
(-p0 + 3.0f * p1 - 3.0f * p2 + p3) * t3);
return x;
}
Mat CalcCatmull(Mat &src, int zoom)
{
int v1, v2, v3, v4, Ptr, Xmax, Ymax;
float Result, t, c1, c2, c3, c4;
//------------------------------------------------------------
Xmax = src.cols;
Ymax = src.rows;
Size srcSize(zoom*Xmax, Ymax);
Mat dst(srcSize, CV_8UC1);
for (int j = 0; j < Ymax; j++)
{
Ptr = 0;
for (int i = 0; i < Xmax; i++)
{
v1 = i - 1; v2 = i; v3 = i + 1; v4 = i + 2;
if (i - 1 < 0) v1 = 0;
if (Xmax <= i + 1) v3 = Xmax - 1;
if (Xmax <= i + 2) v4 = Xmax - 1;
for (double J = 1; J <= zoom; J++)
{
t = J / zoom;
Result = 0.0;
c1 = src.at<uchar>(j, v1);
c2 = src.at<uchar>(j, v2);
c3 = src.at<uchar>(j, v3);
c4 = src.at<uchar>(j, v4);
Result = CalCurveInt(t, c1, c2, c3, c4);
dst.at<uchar>(j, Ptr) = abs(Result);
Ptr++;
}
}
}
//------------------------------------------------
Xmax = dst.cols;
Ymax = dst.rows;
Size srcSize1(Xmax, zoom*Ymax);
Mat dest(srcSize1, CV_8UC1);
for (int i = 0; i < Xmax; i++)
{
Ptr = 0;
for (int j = 0; j < Ymax; j++)
{
v1 = j - 1; v2 = j; v3 = j + 1; v4 = j + 2;
if (j - 1 < 0) v1 = 0;
if (Ymax <= j + 1) v3 = Ymax - 1;
if (Ymax <= j + 2) v4 = Ymax - 1;
for (double J = 1; J <= zoom; J++)
{
t = J / zoom;
Result = 0.0;
c1 = dst.at<uchar>(v1, i);
c2 = dst.at<uchar>(v2, i);
c3 = dst.at<uchar>(v3, i);
c4 = dst.at<uchar>(v4, i);
Result = CalCurveInt(t, c1, c2, c3, c4);
dest.at<uchar>(Ptr, i) = Result;
Ptr++;
}
}
}
return dest;
}
float zoom = 2.0;
int main()
{
Mat src = imread("fruits.png", CV_LOAD_IMAGE_GRAYSCALE);
int width = src.cols;
int hight = src.rows;
/*Image Decimation*/
Size srcdSize(int(width / zoom), int(hight / zoom));
Mat srcd;
pyrDown(src, srcd, srcdSize);
imshow("decimation", srcd);
Mat dst = CalcCatmull(srcd, zoom);
imshow("Image Source", src);
imshow("Image dest", dst);
imwrite("Image dest.png", dst);
waitKey(0);
return 0;
}
Thanks in advance.
My old implementation, seems it worked fine.
#include <iostream>
#include <vector>
#include <stdio.h>
#include <stdarg.h>
#include "opencv2/opencv.hpp"
#include "fstream"
#include "iostream"
using namespace std;
using namespace cv;
//-----------------------------------------------------------------------------------------------------
// Take 2 points, compute values between p1 and p2, p0 and p3 need for tangents computation
// on the bouunds. Parameter t - changes in range 0 to 1 (0 - we are in p1, 1 - we are in p2)
//-----------------------------------------------------------------------------------------------------
void PointOnCurve(Point2f &out, float t, Point2f p0, Point2f p1, Point2f p2, Point2f p3)
{
float t2 = t * t;
float t3 = t2 * t;
out.x = 0.5f * ( ( 2.0f * p1.x ) + ( -p0.x + p2.x ) * t +
( 2.0f * p0.x - 5.0f * p1.x + 4 * p2.x - p3.x ) * t2 +
( -p0.x + 3.0f * p1.x - 3.0f * p2.x + p3.x ) * t3 );
out.y = 0.5f * ( ( 2.0f * p1.y ) + ( -p0.y + p2.y ) * t +
( 2.0f * p0.y - 5.0f * p1.y + 4 * p2.y - p3.y ) * t2 +
( -p0.y + 3.0f * p1.y - 3.0f * p2.y + p3.y ) * t3 );
}
//-----------------------------------------------------------------------------------------------------
// interpolation of 4х4 patch
//
// S * S * S * S
// * * * * * * *
// S * S * S * S
// * * * * * * *
// S * S * S * S
// * * * * * * *
// S * S * S * S
//
// S- pixels of source imgage
//
// sequentially take 2 middle columns and computte D.
//
// S * 1 * 2 * S
// * * * * * * *
// S * 1 * 2 * S
// * * D * D * *
// S * 1 * 2 * S
// * * * * * * *
// S * 1 * 2 * S
//
// same for rows and we will have F
//
// S * S * S * S
// * * * * * * *
// 3 * 3 F 3 * 3
// * * D * D * *
// 4 * 4 F 4 * 4
// * * * * * * *
// S * S * S * S
//
// then compute diagonals and after averafing with neihbours will find С
//
// 1 * S * S * 2
// * * * * * * *
// S * 1 F 2 * S
// * * D C D * *
// S * 2 F 1 * S
// * * * * * * *
// 2 * S * S * 1
//-----------------------------------------------------------------------------------------------------
void PointOnSurface(Mat& src,Mat& dst)
{
float t=0.5;
Point2f out;
dst=Mat(3,3,CV_32FC1);
// Угловые точки результата совпадают с точками центральной ячейки исходного патча
dst.at<float>(0,0)=src.at<float>(1,1);
dst.at<float>(2,0)=src.at<float>(2,1);
dst.at<float>(0,2)=src.at<float>(1,2);
dst.at<float>(2,2)=src.at<float>(2,2);
Point2f p0;
Point2f p1;
Point2f p2;
Point2f p3;
p0.x=0;p0.y=src.at<float>(0,1);
p1.x=1;p1.y=src.at<float>(1,1);
p2.x=2;p2.y=src.at<float>(2,1);
p3.x=3;p3.y=src.at<float>(3,1);
PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(1,0)=out.y;
p0.x=0;p0.y=src.at<float>(0,2);
p1.x=1;p1.y=src.at<float>(1,2);
p2.x=2;p2.y=src.at<float>(2,2);
p3.x=3;p3.y=src.at<float>(3,2);
PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(1,2)=out.y;
p0.x=0;p0.y=src.at<float>(1,0);
p1.x=1;p1.y=src.at<float>(1,1);
p2.x=2;p2.y=src.at<float>(1,2);
p3.x=3;p3.y=src.at<float>(1,3);
PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(0,1)=out.y;
p0.x=0;p0.y=src.at<float>(2,0);
p1.x=1;p1.y=src.at<float>(2,1);
p2.x=2;p2.y=src.at<float>(2,2);
p3.x=3;p3.y=src.at<float>(2,3);
PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(2,1)=out.y;
// diagonals
// 1
p0.x=0;p0.y=src.at<float>(0,0);
p1.x=1;p1.y=src.at<float>(1,1);
p2.x=2;p2.y=src.at<float>(2,2);
p3.x=3;p3.y=src.at<float>(3,3);
PointOnCurve(out,t,p0,p1,p2,p3);
float d1=out.y;
// 2
p0.x=0;p0.y=src.at<float>(3,0);
p1.x=1;p1.y=src.at<float>(2,1);
p2.x=2;p2.y=src.at<float>(1,2);
p3.x=3;p3.y=src.at<float>(0,3);
PointOnCurve(out,t,p0,p1,p2,p3);
float d2=out.y;
// averaging
dst.at<float>(1,1)=1.0/6.0*(d1+d2+dst.at<float>(0,1)+dst.at<float>(1,0)+dst.at<float>(1,2)+dst.at<float>(2,1));
}
//-----------------------------------------------------------------------------------------------------
//
//-----------------------------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------------------------
void Scale2Times(Mat& src_img,Mat &dstImg)
{
Mat imgf,img;
Mat dst;
Mat src;
src_img.convertTo(imgf,CV_32FC1,1.0/255.0);
cv::copyMakeBorder(imgf,img,1,1,1,1,cv::BORDER_REFLECT);
dstImg=Mat(src_img.rows*2,src_img.cols*2,CV_32FC1);
for(int i=0;i<img.rows-4;i++)
{
for(int j=0;j<img.cols-4;j++)
{
img(Rect(j,i,4,4)).copyTo(src);
PointOnSurface(src,dst);
dst.copyTo(dstImg(Rect(2*j+1,2*i+1,3,3)));
}
}
dstImg=dstImg(Rect(0,0,dstImg.cols-2,dstImg.rows-2)).clone();
}
//-----------------------------------------------------------------------------------------------------
//
//-----------------------------------------------------------------------------------------------------
int main( int argc, char** argv )
{
namedWindow("Src");
namedWindow("cvResize");
namedWindow("Catmul-Rom");
Mat Img=imread("C:\\ImagesForTest\\1.tiff",0);
imshow("Src",Img);
Mat dstImg;
Scale2Times(Img,dstImg);
imshow("Catmul-Rom",dstImg);
Mat ImgLin(Img.rows*2,Img.cols*2,CV_8UC1);
cv::resize(Img,ImgLin,Size(Img.cols*2,Img.rows*2),INTER_CUBIC);
imshow("cvResize",ImgLin);
waitKey(0);
//getchar();
return 0;
}
I have 3 vectors in 3D space. Let's call them xaxis, yaxis, and zaxis. These vectors are centered about an arbitrary point somewhere in 3D space. I am interested in rotating the xaxis and yaxis vectors about the zaxis vector a number of degrees θ.
For the following code with values being arbitrary and unimportant:
double xaxis[3], yaxis[3], zaxis[3], point[3], theta;
How would I go about rotating xaxis and yaxis about the zaxis by theta degrees?
Future Note: These attempts do not work. See my answer for the proper solution, which was found with the help of BlueRaja-DannyPflughoeft
My attempt at matrix-based rotation:
double rx[3][3];
double ry[3][3];
double rz[3][3];
double r[3][3];
rx[0][0] = 1;
rx[0][1] = 0;
rx[0][2] = 0;
rx[1][0] = 0;
rx[1][1] = cos(theta);
rx[1][2] = sin(theta);
rx[2][0] = 0;
rx[2][1] = -1.0 * sin(theta);
rx[2][2] = cos(theta);
ry[0][0] = cos(theta);
ry[0][1] = 0;
ry[0][2] = -1.0 * sin(theta);
ry[1][0] = 0;
ry[1][1] = 1;
ry[1][2] = 0;
ry[2][0] = sin(theta);
ry[2][1] = 0;
ry[2][2] = cos(theta);
//No rotation wanted on the zaxis
rz[0][0] = cos(0);
rz[0][1] = sin(0);
rz[0][2] = 0;
rz[1][0] = -1.0 * sin(0);
rz[1][1] = cos(0);
rz[1][2] = 0;
rz[2][0] = 0;
rz[2][1] = 0;
rz[2][2] = 1;
vtkMath::Multiply3x3(rx, ry, r); //Multiplies rx by ry and stores into r
vtkMath::Multiply3x3(r, rz, r); //Multiplies r by rz and stores into r
vtkMath::Multiply3x3(r, xaxis, xaxis);//multiplies a 3x3 by a 3x1
vtkMath::Multiply3x3(r, yaxis, yaxis);//multiplies a 3x3 by a 3x1
This attempt only worked when the plane was in the x-y plane:
double x, y;
x = xaxis[0];
y = xaxis[1];
xaxis[0] = x * cos(theta) - y * sin(theta);
xaxis[1] = x * sin(theta) + y * cos(theta);
x = yaxis[0];
y = yaxis[1];
yaxis[0] = x * cos(theta) - y * sin(theta);
yaxis[1] = x * sin(theta) + y * cos(theta);
Using the axis-angle approach given by BlueRaja-DannyPflughoeft:
double c = cos(theta);
double s = sin(theta);
double C = 1.0 - c;
double Q[3][3];
Q[0][0] = xaxis[0] * xaxis[0] * C + c;
Q[0][1] = xaxis[1] * xaxis[0] * C + xaxis[2] * s;
Q[0][2] = xaxis[2] * xaxis[0] * C - xaxis[1] * s;
Q[1][0] = xaxis[1] * xaxis[0] * C - xaxis[2] * s;
Q[1][1] = xaxis[1] * xaxis[1] * C + c;
Q[1][2] = xaxis[2] * xaxis[1] * C + xaxis[0] * s;
Q[2][0] = xaxis[1] * xaxis[2] * C + xaxis[1] * s;
Q[2][1] = xaxis[2] * xaxis[1] * C - xaxis[0] * s;
Q[2][2] = xaxis[2] * xaxis[2] * C + c;
double x = Q[2][1] - Q[1][2], y = Q[0][2] - Q[2][0], z = Q[1][0] - Q[0][1];
double r = sqrt(x * x + y * y + z * z);
//xaxis[0] /= r;
//xaxis[1] /= r;
//xaxis[2] /= r;
xaxis[0] = x;// ?
xaxis[1] = y;
xaxis[2] = z;
Thanks to BlueRaja - Danny Pflughoeft:
double c = cos(theta);
double s = sin(theta);
double C = 1.0 - c;
double Q[3][3];
Q[0][0] = zaxis[0] * zaxis[0] * C + c;
Q[0][1] = zaxis[1] * zaxis[0] * C + zaxis[2] * s;
Q[0][2] = zaxis[2] * zaxis[0] * C - zaxis[1] * s;
Q[1][0] = zaxis[1] * zaxis[0] * C - zaxis[2] * s;
Q[1][1] = zaxis[1] * zaxis[1] * C + c;
Q[1][2] = zaxis[2] * zaxis[1] * C + zaxis[0] * s;
Q[2][0] = zaxis[0] * zaxis[2] * C + zaxis[1] * s;
Q[2][1] = zaxis[2] * zaxis[1] * C - zaxis[0] * s;
Q[2][2] = zaxis[2] * zaxis[2] * C + c;
xaxis[0] = xaxis[0] * Q[0][0] + xaxis[0] * Q[0][1] + xaxis[0] * Q[0][2];
xaxis[1] = xaxis[1] * Q[1][0] + xaxis[1] * Q[1][1] + xaxis[1] * Q[1][2];
xaxis[2] = xaxis[2] * Q[2][0] + xaxis[2] * Q[2][1] + xaxis[2] * Q[2][2]; // Multiply a 3x3 by 3x1 and store it as the new rotated axis
yaxis[0] = yaxis[0] * Q[0][0] + yaxis[0] * Q[0][1] + yaxis[0] * Q[0][2];
yaxis[1] = yaxis[1] * Q[1][0] + yaxis[1] * Q[1][1] + yaxis[1] * Q[1][2];
yaxis[2] = yaxis[2] * Q[2][0] + yaxis[2] * Q[2][1] + yaxis[2] * Q[2][2]; // Multiply a 3x3 by 3x1 and store it as the new rotated axis
I see that following matrix multiplication is wrong!
As stated above it can be factored with xaxis[0]
xaxis[0] = xaxis[0] * Q[0][0] + xaxis[0] * Q[0][1] + xaxis[0] * Q[0][2];
xaxis[0] = xaxis[0] * (Q[0][0] + Q[0][1] + Q[0][2]);
This does not look like a matrix multiplication. It should be:
xaxis1[0] = xaxis[0] * Q[0][0] + xaxis[1] * Q[0][1] + xaxis[2] * Q[0][2];
xaxis1[1] = xaxis[0] * Q[1][0] + xaxis[1] * Q[1][1] + xaxis[2] * Q[1][2];
xaxis1[2] = xaxis[0] * Q[2][0] + xaxis[1] * Q[2][1] + xaxis[2] * Q[2][2]; // Multiply a 3x3 by 3x1 and store it as the new rotated axis
yaxis1[0] = yaxis[0] * Q[0][0] + yaxis[1] * Q[0][1] + yaxis[2] * Q[0][2];
yaxis1[1] = yaxis[0] * Q[1][0] + yaxis[1] * Q[1][1] + yaxis[2] * Q[1][2];
yaxis1[2] = yaxis[0] * Q[2][0] + yaxis[1] * Q[2][1] + yaxis[2] * Q[2][2]; // Multiply a 3x3 by 3x1 and store it as the new rotated axis
I'm working on an algorithm to generate point to point linear gradients. I have a rough proof of concept implementation done:
GLuint OGLENGINEFUNCTIONS::CreateGradient( std::vector<ARGBCOLORF> &input,POINTFLOAT start, POINTFLOAT end, int width, int height,bool radial )
{
std::vector<POINT> pol;
std::vector<GLubyte> pdata(width * height * 4);
std::vector<POINTFLOAT> linearpts;
std::vector<float> lookup;
float distance = GetDistance(start,end);
RoundNumber(distance);
POINTFLOAT temp;
float incr = 1 / (distance + 1);
for(int l = 0; l < 100; l ++)
{
POINTFLOAT outA;
POINTFLOAT OutB;
float dirlen;
float perplen;
POINTFLOAT dir;
POINTFLOAT ndir;
POINTFLOAT perp;
POINTFLOAT nperp;
POINTFLOAT perpoffset;
POINTFLOAT diroffset;
dir.x = end.x - start.x;
dir.y = end.y - start.y;
dirlen = sqrt((dir.x * dir.x) + (dir.y * dir.y));
ndir.x = static_cast<float>(dir.x * 1.0 / dirlen);
ndir.y = static_cast<float>(dir.y * 1.0 / dirlen);
perp.x = dir.y;
perp.y = -dir.x;
perplen = sqrt((perp.x * perp.x) + (perp.y * perp.y));
nperp.x = static_cast<float>(perp.x * 1.0 / perplen);
nperp.y = static_cast<float>(perp.y * 1.0 / perplen);
perpoffset.x = static_cast<float>(nperp.x * l * 0.5);
perpoffset.y = static_cast<float>(nperp.y * l * 0.5);
diroffset.x = static_cast<float>(ndir.x * 0 * 0.5);
diroffset.y = static_cast<float>(ndir.y * 0 * 0.5);
outA.x = end.x + perpoffset.x + diroffset.x;
outA.y = end.y + perpoffset.y + diroffset.y;
OutB.x = start.x + perpoffset.x - diroffset.x;
OutB.y = start.y + perpoffset.y - diroffset.y;
for (float i = 0; i < 1; i += incr)
{
temp = GetLinearBezier(i,outA,OutB);
RoundNumber(temp.x);
RoundNumber(temp.y);
linearpts.push_back(temp);
lookup.push_back(i);
}
for (unsigned int j = 0; j < linearpts.size(); j++) {
if(linearpts[j].x < width && linearpts[j].x >= 0 &&
linearpts[j].y < height && linearpts[j].y >=0)
{
pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 0] = (GLubyte) j;
pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 1] = (GLubyte) j;
pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 2] = (GLubyte) j;
pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 3] = (GLubyte) 255;
}
}
lookup.clear();
linearpts.clear();
}
return CreateTexture(pdata,width,height);
}
It works as I would expect most of the time, but at certain angles it produces little white dots. I can't figure out what does this.
This is what it looks like at most angles (good) http://img9.imageshack.us/img9/5922/goodgradient.png
But once in a while it looks like this (bad): http://img155.imageshack.us/img155/760/badgradient.png
What could be causing the white dots?
Is there maybe also a better way to generate my gradients if no solution is possible for this?
Thanks
I think you have a bug indexing into the pdata byte vector. Your x domain is [0, width) but when you multiply out the indices you're doing x * 4 * width. It should probably be x * 4 + y * 4 * width or x * 4 * height + y * 4 depending on whether you're data is arranged row or column major.