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page.title=Applying Projection and Camera Views
parent.title=Displaying Graphics with OpenGL ES
previous.title=Drawing Shapes
next.title=Applying Projection and Camera Views
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<h2>This lesson teaches you to</h2>
<li><a href="#projection">Define a Projection</a></li>
<li><a href="#camera-view">Define a Camera View</a></li>
<li><a href="#transform">Apply Projection and Camera Transformations</a></li>
<h2>You should also read</h2>
<li><a href="{@docRoot}guide/topics/graphics/opengl.html">OpenGL</a></li>
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<a href="{@docRoot}shareables/training/"
class="button">Download the sample</a>
<p class="filename"></p>
<p>In the OpenGL ES environment, projection and camera views allow you to display drawn objects in a
way that more closely resembles how you see physical objects with your eyes. This simulation of
physical viewing is done with mathematical transformations of drawn object coordinates:</p>
<li><em>Projection</em> - This transformation adjusts the coordinates of drawn objects based on
the width and height of the {@link android.opengl.GLSurfaceView} where they are displayed. Without
this calculation, objects drawn by OpenGL ES are skewed by the unequal proportions of the view
window. A projection transformation typically only has to be calculated when the proportions of the
OpenGL view are established or changed in the {@link
onSurfaceChanged()} method of your renderer. For more information about OpenGL ES projections and
coordinate mapping, see <a
href="{@docRoot}guide/topics/graphics/opengl.html#coordinate-mapping">Mapping Coordinates for Drawn
<li><em>Camera View</em> - This transformation adjusts the coordinates of drawn objects based on a
virtual camera position. Its important to note that OpenGL ES does not define an actual camera
object, but instead provides utility methods that simulate a camera by transforming the display of
drawn objects. A camera view transformation might be calculated only once when you establish your
{@link android.opengl.GLSurfaceView}, or might change dynamically based on user actions or your
applications function.</li>
<p>This lesson describes how to create a projection and camera view and apply it to shapes drawn in
your {@link android.opengl.GLSurfaceView}.</p>
<h2 id="projection">Define a Projection</h2>
<p>The data for a projection transformation is calculated in the {@link
android.opengl.GLSurfaceView.Renderer#onSurfaceChanged onSurfaceChanged()}
method of your {@link android.opengl.GLSurfaceView.Renderer} class. The following example code
takes the height and width of the {@link android.opengl.GLSurfaceView} and uses it to populate a
projection transformation {@link android.opengl.Matrix} using the {@link
android.opengl.Matrix#frustumM Matrix.frustumM()} method:</p>
// mMVPMatrix is an abbreviation for "Model View Projection Matrix"
private final float[] mMVPMatrix = new float[16];
private final float[] mProjectionMatrix = new float[16];
private final float[] mViewMatrix = new float[16];
public void onSurfaceChanged(GL10 unused, int width, int height) {
GLES20.glViewport(0, 0, width, height);
float ratio = (float) width / height;
// this projection matrix is applied to object coordinates
// in the onDrawFrame() method
Matrix.frustumM(mProjectionMatrix, 0, -ratio, ratio, -1, 1, 3, 7);
<p>This code populates a projection matrix, {@code mProjectionMatrix} which you can then combine
with a camera view transformation in the {@link android.opengl.GLSurfaceView.Renderer#onDrawFrame
onDrawFrame()} method, which is shown in the next section.</p>
<p class="note"><strong>Note:</strong> Just applying a projection transformation to your
drawing objects typically results in a very empty display. In general, you must also apply a camera
view transformation in order for anything to show up on screen.</p>
<h2 id="camera-view">Define a Camera View</h2>
<p>Complete the process of transforming your drawn objects by adding a camera view transformation as
part of the drawing process in your renderer. In the following example code, the camera view
transformation is calculated using the {@link android.opengl.Matrix#setLookAtM Matrix.setLookAtM()}
method and then combined with the previously calculated projection matrix. The combined
transformation matrices are then passed to the drawn shape.</p>
public void onDrawFrame(GL10 unused) {
// Set the camera position (View matrix)
Matrix.setLookAtM(mViewMatrix, 0, 0, 0, -3, 0f, 0f, 0f, 0f, 1.0f, 0.0f);
// Calculate the projection and view transformation
Matrix.multiplyMM(mMVPMatrix, 0, mProjectionMatrix, 0, mViewMatrix, 0);
// Draw shape
<h2 id="#transform">Apply Projection and Camera Transformations</h2>
<p>In order to use the combined projection and camera view transformation matrix shown in the
previews sections, first add a matrix variable to the <em>vertex shader</em> previously defined
in the <code>Triangle</code> class:</p>
public class Triangle {
private final String vertexShaderCode =
// This matrix member variable provides a hook to manipulate
// the coordinates of the objects that use this vertex shader
<strong>"uniform mat4 uMVPMatrix;" +</strong>
"attribute vec4 vPosition;" +
"void main() {" +
// the matrix must be included as a modifier of gl_Position
// Note that the uMVPMatrix factor *must be first* in order
// for the matrix multiplication product to be correct.
" gl_Position = <strong>uMVPMatrix</strong> * vPosition;" +
// Use to access and set the view transformation
private int mMVPMatrixHandle;
<p>Next, modify the {@code draw()} method of your graphic objects to accept the combined
transformation matrix and apply it to the shape:</p>
public void draw(float[] mvpMatrix) { // pass in the calculated transformation matrix
// get handle to shape's transformation matrix
<strong>mMVPMatrixHandle = GLES20.glGetUniformLocation(mProgram, "uMVPMatrix");</strong>
// Pass the projection and view transformation to the shader
<strong>GLES20.glUniformMatrix4fv(mMVPMatrixHandle, 1, false, mvpMatrix, 0);</strong>
// Draw the triangle
GLES20.glDrawArrays(GLES20.GL_TRIANGLES, 0, vertexCount);
// Disable vertex array
<p>Once you have correctly calculated and applied the projection and camera view transformations,
your graphic objects are drawn in correct proportions and should look like this:</p>
<img src="{@docRoot}images/opengl/ogl-triangle-projected.png">
<p class="img-caption">
<strong>Figure 1.</strong> Triangle drawn with a projection and camera view applied.</p>
<p>Now that you have an application that displays your shapes in correct proportions, it's time to
add motion to your shapes.</p>