I need to render a couple of cubes by opengl, and the color of every cube depends on the the magnetic field at the center of cube, but I don't know how to convert the float number into the QVector3D or glm::vec3 (RGB).
And I can convert the range of the float array between 0 and 1， I need to know how to convert the magnetic field array to RGB to define the color array.
If I understand correctly, then you want to represent a floating point value in the range [0.0, 1.0], by a RGB color.
I recommend to transform the value to the HSV color range.
For the full range the conversion is:
float value = ...; // value in range [0.0, 1.0]
float H = value;
float R = fabs(H * 6.0f - 3.0f) - 1.0f;
float G = 2.0f - fabs(H * 6.0f - 2.0f);
float B = 2.0f - fabs(H * 6.0f - 4.0f);
glm::vec3 color(
std::max(0.0, std::min(1.0, R))
std::max(0.0, std::min(1.0, G))
std::max(0.0, std::min(1.0, B)));
If you don't want the full range, for example, if you want to use the range from red to blue, then value has to be scaled:
float H = value * 2.0f/3.0f;
You need some form of lookup table (LUT). A RGB vector has 3 dimensions, a single float just one. There's literally an infinite number of ways how to map between those two.
Related
I've generated a geodesic sphere for opengl rendering following a question on here and I'm trying to put texture on it. I came up with the following code by reversing an algorithm for a point on a sphere:
//complete circle equation is as follows
///<Summary>
///x = r * sin(s) * sin(t)
///y = r* cos(t)
///z = r * cos(s) * sin(t)
///</Summary>
float radius = 1.0f;
//T (height/latitude) angle
float angleT = acos(point.y / radius) ;
//S (longitude )angle
float angleS = ( asin(point.x / (radius * sin(angleT)))) + (1.0f* M_PI);
float angleS2 =( acos(point.z / (radius * sin(angleT)))) + (1.0f * M_PI);
//Angle can be 0-PI (0-180 degs), divide by this to get 0-1
angleT = angleT / (M_PI);
//Angle can be 0-2PI (0-360 degs)S
angleS = angleS / ( M_PI *2 );
angleS2 = angleS2 / ( M_PI *2 );
//Flip the y co-ord
float yTex = 1 - angleT;
float xTex = 0.0f;
//I have found that angleS2 is valid 0.5-1.0, and angleS is valid (0.3-0.5)
if (angleS < 0.5f)
{
xTex = angleS;
}
else
{
xTex = angleS2;
}
return glm::vec2( xTex , yTex);
As you can see, I've found that both versions of calculating the S angle have limited valid ranges.
float angleS = ( asin(point.x / (radius * sin(angleT)))) + (1.0f* M_PI);
float angleS2 =( acos(point.z / (radius * sin(angleT)))) + (1.0f * M_PI);
S1 is gives valid answers between x texture co-ords 0.3 and 0.5 and S2 gives valid answers for between x texture co-ords 0.5 and 1.0 (Conversion to co-ords omitted above but present in first code example). Why is it that neither formula is giving me valid answers for under 0.3?
Thanks
Will
Correct on this side
The weird border between working and not, probably caused by opengl's interpolation
Reversed section
The image being used
Edit: Here is the seam
The equations you use to calculate the longitude angles are not correct seeing what you are trying to accomplish. For the longitude angle, the range you require is 0-360 degrees, which can not be obtained through asin or acos functions, because those functions only return results between -90 and 90 degrees or 0 to 180 degrees. You can, however, use the atan2 function, which returns values from the correct interval. The code I've been working with for the past 2 years is the following:
float longitude = atan2f(point.x, point.z) + (float)M_PI;
This equation will map the horizontal center of the texture in the direction of positive Z axis. If you want the horizontal center of the texture to be in the direction of positive X axis, add M_PI / 2.0.
I have a set of different colors expressed in RGB float values in the unit intervall, i.e. red for instance is
glColor4f(1.f, 0.f, 0.f, 1.f);
with the fourth value being the alpha channel.
No I would like to adjust this color heatmap-style, i.e. pixels with an underlying scalar value close to 1 are appearing more intense than pixels with an underlying value near 0.
I chose this procedure
float red{ value <= 0.57147f ? 446.22f * value / 255.f : 1.f };
float green{ value <= 0.95f ? ((value - 0.6f) * 728.57f) / 255.f : 1.f };
float blue{ 0.f };
My question is now, how I can generate a similar rgb distribution for several discrete colors, e.g. blue, purple, yellow, etc.
Let's say there is a grid terrain for a game composed of tiles made of two triangles - made from four vertices. How would we find the Y (up) position of a point between the four vertices?
I have tried this:
float diffZ1 = lerp(heights[0], heights[2], zOffset);
float diffZ2 = lerp(heights[1], heights[3], zOffset);
float yPosition = lerp(diffZ1, diffZ2, xOffset);
Where z/yOffset is the z/y offset from the first vertex of the tile in percent / 100. This works for flat surfaces but not so well on bumpy terrain.
I expect this has something to do with the terrain being made from triangles where the above may work on flat planes. I'm not sure, but does anybody know what's going wrong?
This may better explain what's going on here:
In the code above "heights[]" is an array of the Y coordinate of surrounding vertices v0-3.
Triangle 1 is made of vertex 0, 2 and 1.
Triangle 2 is made of vertex 1, 2 and 3.
I wish to find coordinate Y of p1 when its x,y coordinates lay between v0-3.
So I have tried determining which triangle the point is between through this function:
bool PointInTriangle(float3 pt, float3 pa, float3 pb, float3 pc)
{
// Compute vectors
float2 v0 = pc.xz - pa.xz;
float2 v1 = pb.xz - pa.xz;
float2 v2 = pt.xz - pa.xz;
// Compute dot products
float dot00 = dot(v0, v0);
float dot01 = dot(v0, v1);
float dot02 = dot(v0, v2);
float dot11 = dot(v1, v1);
float dot12 = dot(v1, v2);
// Compute barycentric coordinates
float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
// Check if point is in triangle
return (u >= 0.0f) && (v >= 0.0f) && (u + v <= 1.0f);
}
This isn't giving me the results I expected
I am then trying to find the y coordinate of point p1 inside each triangle:
// Position of point p1
float3 pos = input[0].PosI;
// Calculate point and normal for triangles
float3 p1 = tile[0];
float3 n1 = (tile[2] - p1) * (tile[1] - p1); // <-- Error, cross needed
// = cross(tile[2] - p1, tile[1] - p1);
float3 p2 = tile[3];
float3 n2 = (tile[2] - p2) * (tile[1] - p2); // <-- Error
// = cross(tile[2] - p2, tile[1] - p2);
float newY = 0.0f;
// Determine triangle & get y coordinate inside correct triangle
if(PointInTriangle(pos, tile[0], tile[1], tile[2]))
{
newY = p1.y - ((pos.x - p1.x) * n1.x + (pos.z - p1.z) * n1.z) / n1.y;
}
else if(PointInTriangle(input[0].PosI, tile[3], tile[2], tile[1]))
{
newY = p2.y - ((pos.x - p2.x) * n2.x + (pos.z - p2.z) * n2.z) / n2.y;
}
Using the following to find the correct triangle:
if((1.0f - xOffset) <= zOffset)
inTri1 = true;
And correcting the code above to use the correct cross function seems to have solved the problem.
Because your 4 vertices may not be on a plane, you should consider each triangle separately. First find the triangle that the point resides in, and then use the following StackOverflow discussion to solve for the Z value (note the different naming of the axes). I personally like DanielKO's answer much better, but the accepted answer should work too:
Linear interpolation of three 3D points in 3D space
EDIT: For the 2nd part of your problem (finding the triangle that the point is in):
Because the projection of your tiles onto the xz plane (as you define your coordinates) are perfect squares, finding the triangle that the point resides in is a very simple operation. Here I'll use the terms left-right to refer to the x axis (from lower to higher values of x) and bottom-top to refer to the z axis (from lower to higher values of z).
Each tile can only be split in one of two ways. Either (A) via a diagonal line from the bottom-left corner to the top-right corner, or (B) via a diagonal line from the bottom-right corner to the top-left corner.
For any tile that's split as A:
Check if x' > z', where x' is the distance from the left edge of the tile to the point, and z' is the distance from the bottom edge of the tile to the point. If x' > z' then your point is in the bottom-right triangle; otherwise it's in the upper-left triangle.
For any tile that's split as B: Check if x" > z', where x" is the distance from the right edge of your tile to the point, and z' is the distance from the bottom edge of the tile to the point. If x" > z' then your point is in the lower-left triangle; otherwise it's in the upper-right triangle.
(Minor note: Above I assume your tiles aren't rotated in the xz plane; i.e. that they are aligned with the axes. If that's not correct, simply rotate them to align them with the axes before doing the above checks.)
Is there a way to calculate the XYZ position in front of a quaternion (XYZW) rotation, preferably using GLM?
I know the Quat rotation and the Position of the object I want to calculate the position in front of.
I know how to calculate the position in front of a rotation matrix where you have a Front vector, Up vector and Right vector, but in this case I only have XYZW values (where W is always 0, I never see it becomming 1..?)
In very short:
The data I have: Quat (X Y Z W) and Position(X Y Z) and I want to calculate PositionInFront(Position, Quat, Distance, &X, &Y, &Z)
How to accomplish this goal?
I tried a cast to 3x3matrix and perform the Up,Right,Front (because a 3x3 matrix cast is these values, right?) calculations but they do not return the correct positions.
Or would it be possible to determine the objects Z Angle? (rotation around world Z / height axis only)
It seemed that there were 2 more quaternion structures for the vehicle which I forgot to use. and those 3 are the complete set needed for the Front,Right,Up calculation formula:
float offX = 10.0f;
float offY = 0.0f;
float offZ = 0.0f;
float x = offX * info.Rotation.Front.x + offY * info.Rotation.Right.x + offZ * info.Rotation.Up.x + info.Pos.x;
float y = offX * info.Rotation.Front.y + offY * info.Rotation.Right.y + offZ * info.Rotation.Up.y + info.Pos.y;
float z = offX * info.Rotation.Front.z + offY * info.Rotation.Right.z + offZ * info.Rotation.Up.z + info.Pos.z;
float Angle = (atan2(x-info.Pos.x, y-info.Pos.y) * 180.0f / PI);
I have defined 2 points on the surface of a sphere using spherical coordinates.
// define end point positions
float theta_point_1 = (5/10.0)*M_PI;
float phi_point_1 = (5/10.0)*2*M_PI;
float x_point_1 = Radius * sin(theta_point_1) * cos(phi_point_1);
float y_point_1 = Radius * sin(theta_point_1) * sin(phi_point_1);
float z_point_1 = Radius * cos(theta_point_1);
float theta_point_2 = (7/10.0)*M_PI;
float phi_point_2 = (1/10.0)*2*M_PI;
float x_point_2 = Radius * sin(theta_point_2) * cos(phi_point_2);
float y_point_2 = Radius * sin(theta_point_2) * sin(phi_point_2);
float z_point_2 = Radius * cos(theta_point_2);
// draw end points
void end_points ()
{
glColor3f (1.0, 1.0, 1.0);
glPointSize(25.0);
glBegin(GL_POINTS);
glVertex3f(x_point_1,y_point_1,z_point_1);
glVertex3f(x_point_2,y_point_2,z_point_2);
glEnd();
}
To step between the two points, I do the following:
find the difference between theta_points_1,2 and phi_points_1,2
divide the differences by 'n' (yielding 's')
redraw 'n' times, while stepping up the theta and phi by 's' each time
In the following, I've defined the differences between my theta and phi values, divided them, and then redraw them.
// begining spherical coords
float theta_point_1_value=5;
float phi_point_1_value=5;
// ending sperical coords
float theta_point_2_value=7;
float phi_point_2_value=1;
// dividing the difference evenly
float step_points=30;
float step_theta = 2/step_points;
float step_phi = 4/step_points;
// step between spherical coordinates
void stepping_points ()
{
glColor3f (1.0, 0.0, 0.0);
for (int i = 1; i < step_points; i++)
{
float theta = (theta_point_1_value/10.0)*M_PI;
float phi = (phi_point_1_value/10.0)*2*M_PI;
float x = Radius * sin(theta) * cos(phi);
float y = Radius * sin(theta) * sin(phi);
float z = Radius * cos(theta);
glPushMatrix();
glTranslatef(x,y,z);
glutSolidSphere (0.05,10,10);
glPopMatrix();
}
glEnd();
}
Now I understand, this displays 30 solid spheres at the same position. Because I have NOT included 'step_theta' or 'step_phi' in any of the redraws.
And that is the root of my question. How do I employ 'step_theta' and 'step_phi' in my redraws?
What I want to do is say something like this at the top of my 'for' loop:
for (int i = 1; i < step_points; i++)
{
float theta_point_1_value = (theta_point_1_value+step_theta);
float phi_point_1_value = (phi_point_1_value+step_phi);
float theta = (theta_point_1_value/10.0)*M_PI;
float phi = (phi_point_1_value/10.0)*2*M_PI;
float x = Radius * sin(theta) * cos(phi);
float y = Radius * sin(theta) * sin(phi);
float z = Radius * cos(theta);
glPushMatrix();
glTranslatef(x,y,z);
glutSolidSphere (0.05,10,10);
glPopMatrix();
}
The above will redraw 30 solid spheres, but they don't show between my defined end points. It's pretty clear that either my math or syntax is screwy (or more than likely, both are).
Hint: What is the range of your loop variable, i? What do you want the range of your step_theta and step_phi to be?
When you declare a variable inside the loop, it goes out of scope and is destructed after every iteration. As such, only the value of i changes between your loop iterations.
Also: Consider using a vector/point class. (x_point_1, y_point_1) is not C++ :).
If you want consistent timing regardless of frame rate, you need to track the passage of time and use that to control how far you interpolate between the two points. Remember the start time and calculate the desired end time, then each frame, calculate (float)(now-start)/(end-start). This will give you a value between 0.0 and 1.0. Multiply that value by the delta of each spherical coordinate and add their start angles and you'll get what angles you need to be at now.