I'm using the GLM library for OpenGL to render shapes relative to a camera using perspective and modelview matrices. The three camera vectors are as follows:
glm::vec3 cam_pos(0.0f, 0.0f, 20.0f); // e | Position of camera
glm::vec3 cam_look_at(0.0f, 0.0f, -1.0f); // d | This is where the camera looks at
glm::vec3 cam_up(0.0f, 1.0f, 0.0f); // up | What orientation "up" is
The perspective and modelviews are generated via glm functions as follows:
P = glm::perspective(fov, (float)width / (float)height, 0.1f, 1000.0f);
V = glm::lookAt(cam_pos, cam_look_at, cam_up);
I have implemented trackball camera movement to adjust the direction at which the camera is looking.
Now, I'm trying to code a draggable point object that follows the mouse movement according to which way the camera is looking. However, I'm having trouble with the math for doing this.
How would I get the translation matrix to translate the point with inside the GLFW mouse callback given the displacement of the mouse in x and y coordinates and the three camera vectors?
Translate your 3 camera vectors to a Rotation-Translation Matrix (RT). With this RT matrix your can now linear transform any rigid object (basically anything in computer graphics) with respect to your camera location and pose.
Have a look at this http://www.opengl-tutorial.org/beginners-tutorials/tutorial-3-matrices/
Hope this approach helps.
Related
I have been playing around with OpenGL and matrix operations and I understand the concept of P * V * M but I cannot understand why changing the Z position of the 'camera' does not have the effect of zooming.
When using a perspective projection, changing the Z of the camera has the effect of zoom (as i'd expect).
glm::mat4 Projection = glm::perspective(45.0f, 4.0f / 3.0f, 0.1f, 100.0f);
glm::mat4 View = glm::lookAt(
glm::vec3(0,0,3), // changing 3 to 8 will zoom out
glm::vec3(0,0,0),
glm::vec3(0,1,0)
);
glm::mat4 Model = glm::mat4(1.0f);
gml::mat4 MVP = Projection * View * Model;
However, when I use an ortho projection, changing the 3 to 8 or anything it does not have the effect of zooming out. I know they are very different projections but I am looking for an explanation (the math behind why it doesn't work would be especially helpful).
glm::mat4 Projection = glm::ortho(
0.0f,
128.0f,
0.0f,
72.0f,
0.0f,
100.0f
);
That's how orthographic projections work. Let's start with a perspective transform:
You get the projection of an object by following a straight line to the camera:
If you move the camera closer, then you will see that the projected area increases:
Orthographic projections work differently. You get the projection by following a straight line that is perpendicular to the image plane:
And obviously, the size of the projected area does not depend on how far the camera is away from the object. That's because the projection lines will always be parallel and preserve the size of the object in the two directions of the image plane.
When you change the Z coordinate from 3 to 8, you're not actually zooming out, you're just moving the camera farther away. You can zoom out without moving the camera by changing the first parameter for glm::perspective.
An orthographic camera doesn't have a location (you can think of it as infinitely far away), so it's not possible to "move" an orthographic camera in the same way. You can zoom out by changing the bounds passed to glm::ortho. Simply pass larger numbers to glm::ortho.
Look at what happens, when you move perspective camera:
Here: (xe, ye, ze) - point in eye coordinate system. (xp, yp, zp) - projection of that point
n - distance to near plane
t - distance to top plane of frustrum
You can see, that when you approach camera, xp and yp will grow.
In contrast, changing z position of orthogonal camera won't effect xp and yp, but still will effect zp, thus will change value in depth buffer.
How to I obtain the centre of the objects I'm drawing in direct x 11? I'm having a problem when rotating the objects that they're rotating about their position, but their position is from one of the corners, resulting in a circular motion when rotating. I'm trying to rotate about the cente (origin)
I'm translating before rotating using the following:
setObjectWorld(XMMatrixIdentity());
setTranslation(XMMatrixTranslation(getPositionX(), getPositionY(), getPositionZ()));
setRotationAxis(XMVectorSet(0.0f, 1.0f, 0.0f, 0.0f));
setRotation(XMMatrixRotationAxis(getRotationAxisVector(), delta));
setObjectWorld(getTranslationMatrix() * getRotationMatrix());
The outcome is this:
Rotation/scale should be done before translation
I'm despairing of the task to zoom in on the current mouse position in OpenGL. I've tried a lot of different things and read other posts on this, but I couldn't adapt the possible solutions to my specific problem. So as far as I understood it, you'll have to get the current window coordinates of the mouse curser, then unproject them to get world coordinates and finally translate to those world coordinates.
To find the current mouse positions, I use the following code in my GLUT mouse callback function every time the right mouse button is clicked.
if(button == 2)
{
mouse_current_x = x;
mouse_current_y = y;
...
Next up, I unproject the current mouse positions in my display function before setting up the ModelView and Projection matrices, which also seems to work perfectly fine:
// Unproject Window Coordinates
float mouse_current_z;
glReadPixels(mouse_current_x, mouse_current_y, 1, 1, GL_DEPTH_COMPONENT, GL_FLOAT, &mouse_current_z);
glm::vec3 windowCoordinates = glm::vec3(mouse_current_x, mouse_current_y, mouse_current_z);
glm::vec4 viewport = glm::vec4(0.0f, 0.0f, (float)width, (float)height);
glm::vec3 worldCoordinates = glm::unProject(windowCoordinates, modelViewMatrix, projectionMatrix, viewport);
printf("(%f, %f, %f)\n", worldCoordinates.x, worldCoordinates.y, worldCoordinates.z);
Now the translation is where the trouble starts. Currently I'm drawing a cube with dimensions (dimensionX, dimensionY, dimensionZ) and translate to the center of that cube, so my zooming happens to the center point as well. I'm achieving zooming by translating in z-direction (dolly):
// Set ModelViewMatrix
modelViewMatrix = glm::mat4(1.0); // Start with the identity as the transformation matrix
modelViewMatrix = glm::translate(modelViewMatrix, glm::vec3(0.0, 0.0, -translate_z)); // Zoom in or out by translating in z-direction based on user input
modelViewMatrix = glm::rotate(modelViewMatrix, rotate_x, glm::vec3(1.0f, 0.0f, 0.0f)); // Rotate the whole szene in x-direction based on user input
modelViewMatrix = glm::rotate(modelViewMatrix, rotate_y, glm::vec3(0.0f, 1.0f, 0.0f)); // Rotate the whole szene in y-direction based on user input
modelViewMatrix = glm::rotate(modelViewMatrix, -90.0f, glm::vec3(1.0f, 0.0f, 0.0f)); // Rotate the camera by 90 degrees in negative x-direction to get a frontal look on the szene
modelViewMatrix = glm::translate(modelViewMatrix, glm::vec3(-dimensionX/2.0f, -dimensionY/2.0f, -dimensionZ/2.0f)); // Translate the origin to be the center of the cube
glBindBuffer(GL_UNIFORM_BUFFER, globalMatricesUBO);
glBufferSubData(GL_UNIFORM_BUFFER, sizeof(glm::mat4), sizeof(glm::mat4), glm::value_ptr(modelViewMatrix));
glBindBuffer(GL_UNIFORM_BUFFER, 0);
I tried to replace the translation to the center of the cube by translating to the worldCoordinates vector, but this didn't work. I also tried to scale the vector by width or height.
Am I missing out on some essential step here?
Maybe this won't work in your case. But to me this seems like the best way to handle this. Use glulookat() to look at the xyz position of the mouse click that you have already found. Then change the gluPerspective() to a smaller angle of view to achieve the actual zoom.
I am working on rendering a terrain in OpenGL.
My code is the following:
void Render_Terrain(int k)
{
GLfloat angle = (GLfloat) (k/40 % 360);
//PROJECTION
glm::mat4 Projection = glm::perspective(45.0f, 1.0f, 0.1f, 100.0f);
//VIEW
glm::mat4 View = glm::mat4(1.);
//ROTATION
//View = glm::rotate(View, angle * -0.1f, glm::vec3(1.f, 0.f, 0.f));
//View = glm::rotate(View, angle * 0.2f, glm::vec3(0.f, 1.f, 0.f));
//View = glm::rotate(View, angle * 0.9f, glm::vec3(0.f, 0.f, 1.f));
View = glm::translate(View, glm::vec3(0.f,0.f, -4.0f)); // x, y, z position ?
//MODEL
glm::mat4 Model = glm::mat4(1.0);
glm::mat4 MVP = Projection * View * Model;
glUniformMatrix4fv(glGetUniformLocation(shaderprogram, "MVP_matrix"), 1, GL_FALSE, glm::value_ptr(MVP));
//Transfer additional information to the vertex shader
glm::mat4 MV = Model * View;
glUniformMatrix4fv(glGetUniformLocation(shaderprogram, "MV_matrix"), 1, GL_FALSE, glm::value_ptr(MV));
glClearColor(0.0, 0.0, 0.0, 1.0);
glDrawArrays(GL_LINE_STRIP, terrain_start, terrain_end );
}
I can do a rotation around the X,Y,Z axis, scale my terrain but I can't find a way to move the camera. I am using OpenGL 3+ and I am kinda new to graphics.
The best way to move the camera would be through the use of gluLookAt(), it simulates camera movement since the camera cannot be moved whatsoever. The function takes 9 parameters. The first 3 are the XYZ coordinates of the eye which is where the camera is exactly located. The second 3 parameters are the XYZ coordinates of the center which is the point the camera is looking at from the eye. It is always going to be the center of the screen. The third 3 parameters are the XYZ coordinates of the UP vector which points vertically upwards from the eye. Through manipulating those 3 XYZ coordinates you can simulate any camera movement you want.
Check out this link.
Further details:
-If you want for example to rotate around an object you rotate your eye around the up vector.
-If you want to move forward or backwards you add or subtract to the eye as well as the center points.
-If you want to tilt the camera left or right you rotate your up vector around your look vector where your look vector is center - eye.
gluLookAt operates on the deprecated fixed function pipeline, so you should use glm::lookAt instead.
You are currently using a constant vector for translation. In the commented out code (which I assume you were using to test rotation), you use angle to adjust the rotation. You should have a similar variable for translation. Then, you can change the glm::translate call to:
View = glm::translate(View, glm::vec3(x_transform, y_transform, z_transform)); // x, y, z position ?
and get translation.
You should probably pass in more than one parameter into Render_Terrain, as translation and rotation need at least six parameters.
In OpenGL the camera is always at (0, 0, 0). You need to set the matrix mode to GL_MODELVIEW, and then modify or set the model/view matrix using things like glTranslate, glRotate, glLoadMatrix, etc. in order to make it appear that the camera has moved. If you're using GLU, you can use gluLookAt to point the camera in a particular direction.
I've just started playing with OpenGl to render a number of structure each comprising a number of polygon.
Basically I want to perform the equivalent of setting a camera at (0,0,z) in the world (structure) coordinates and rotate it about the x,y and z-axes of the world axes (in that order!) to render a view of each structure (as I understand it it common practice to do use the inverse camera matrix). Thus as I understand it I need to translate (to world origin i.e. (0,0,-z)) * rotateZrotateYrotateX * translate (re-define world origin see below)
So I think I need something like:
//Called when the window is resized
void handleResize(int w, int h) {
glViewport(0, 0, w, h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(9.148, (double)w / (double)h, 800.0, 1500.0);
}
float _Zangle = 10.0f;
float _cameraAngle = 90.0f;
//Draws the 3D scene
void drawScene() {
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_MODELVIEW); //Switch to the drawing perspective
glLoadIdentity(); //Reset the drawing perspective
glTranslatef(0.0f, 0.0f, -z); //Move forward Z (mm) units
glRotatef(-_Zangle, 0.0f, 0.0f, 1.0f); //Rotate "camera" about the z-axis
glRotatef(-_cameraAngle, 0.0f, 1.0f, 0.0f); //Rotate the "camera" by camera_angle about y-axis
glRotatef (90.0f,1.0f,0.0f,0.0f); // rotate "camera" by 90 degrees about x-axis
glTranslatef(-11.0f,189.0f,51.0f); //re-define origin of world coordinates to be (11,-189,-51) - applied to all polygon vertices
glPushMatrix(); //Save the transformations performed thus far
glBegin(GL_POLYGON);
glVertex3f(4.91892,-225.978,-50.0009);
glVertex3f(5.73534,-225.978,-50.0009);
glVertex3f(6.55174,-225.978,-50.0009);
glVertex3f(7.36816,-225.978,-50.0009);
.......// etc
glEnd();
glPopMatrix();
However when I compile and run this the _angle and _cameraAngle seem to be reversed i.e. _angle seems to rotate about y-axis (Vertical) of Viewport and _cameraAngle about z-axis (into plane of Viewport)? What am I doing wrong?
Thanks for taking the time to read this
The short answer is: Use gluLookAt(). This utility function creates the proper viewing matrix.
The longer answer is that each OpenGL transformation call takes the current matrix and multiplies it by a matrix built to accomplish the transformation. By calling a series of OpenGL transformation function you build one transformation matrix that will apply the combination of transformations. Effectively, the matrix will be M = M1 * M2 * M3 . . . Mathematically, the transformations are applied from right to left in the above equation.
Your code doesn't move the camera. It stays at the origin, and looks down the negative z-axis. Your transformations move everything in model space to (11,-189,-51), rotates everything 90 degrees about the x-axis, rotates everything 90 degrees about the y-axis, rotates everything 10 degrees about the z-axis, then translates everything -z along the z-axis.
EDIT: More information
I'm a little confused about what you want to accomplish, but I think you want to have elements at the origin, and have the camera look at those elements. The eye coordinates would be where you want the camera, and the center coordinates would be where you want the objects to be. I'd use a little trigonometry to calculate the position of the camera, and point it at the origin.
In this type of situation I usually keep track of camera position using longitude, latitude, and elevation centered on the origin. Calculating x,y,z for the eye coordinates is simplyx = elv * cos(lat) * sin(lon), y = elv * sin(lat), z = elv * cos(lat) * cos(lat).
My gluLookAt call would be gluLookAt(x, y, z, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
You could rotate the up on the camera by changing the last three coordinates for gluLookAt.
The z axis is coming from the center of the monitor into you. So, rotating around the z-axis should make the camera spin in place (like a 2D rotation on just the xy plane). I can't tell, but is that what's happening here?
It's possible that you are encountering Gimbal Lock. Try removing one of the rotations and see if things work the way they should.
While it's true that you can't actually move the camera in OpenGL, you can simulate camera motion by moving everything else. This is why you hear about the inverse camera matrix. Instead of moving the camera by (0, 0, 10), we can move everything in the world by (0, 0, -10). If you expand those out into matrices, you will find that they are inverses of each other.
I also noticed that, given the code presented, you don't need the glPushMatrix()/glPopMatrix() calls. Perhaps there is code that you haven't shown that requires them.
Finally, can you provide an idea of what it is you are trying to render? Debugging rotations can be hard without some context.
Short answer :Good tip
Longer answer: Yes the order of matrix multiplication is clear... that's what I meant by inverse camera matrix to indicate moving all the world coordinates of structures into the camera coordinates (hence the use of "camera" in my comments ;-)) instead of actually translating and rotating camera into the world coordinates.
So if I read between the lines correctly you suggest something like:
void drawScene() {
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_MODELVIEW); //Switch to the drawing perspective
glLoadIdentity(); //Reset the drawing perspective
gluLookAt(0.0,0.0,z,11.0,-189.0,-51.0,0.0,1.0,0.0); //eye(0,0,z) look at re-defined world origin(11,-189,-51) and up(0.0,1.0,0.0)
glRotatef(-_Zangle, 0.0f, 0.0f, 1.0f); //Rotate "camera" (actually structures) about the z-axis
glRotatef(-_cameraAngle, 0.0f, 1.0f, 0.0f); //Rotate the "camera" (actually structures!) by camera_angle about y-axis
glRotatef (90.0f,1.0f,0.0f,0.0f); // rotate "camera" (actually structures) by 90 degrees about x-axis
glPushMatrix();
Or am I still missing something?
I think you are mixing axes of your world with axes of the camera,
GLRotatef only uses axes of the camera, they are not the same as your the world axes once the camera is rotated.