使用Android MediaCodec和MediaProjection一起进行屏幕录制有以下解决方法：

1. 获取MediaProjection权限： 在AndroidManifest.xml文件中添加以下权限：

   然后在Activity中使用以下代码获取MediaProjection权限：

   private static final int REQUEST_CODE_SCREEN_CAPTURE = 1;
   private MediaProjectionManager mMediaProjectionManager;
   private MediaProjection mMediaProjection;
   
   private void requestScreenCapture() {
       mMediaProjectionManager = (MediaProjectionManager) getSystemService(Context.MEDIA_PROJECTION_SERVICE);
       startActivityForResult(mMediaProjectionManager.createScreenCaptureIntent(), REQUEST_CODE_SCREEN_CAPTURE);
   }
   
   @Override
   protected void onActivityResult(int requestCode, int resultCode, Intent data) {
       if (requestCode == REQUEST_CODE_SCREEN_CAPTURE && resultCode == RESULT_OK) {
           mMediaProjection = mMediaProjectionManager.getMediaProjection(resultCode, data);
           startScreenCapture();
       }
   }
   

2. 创建MediaCodec进行编码：

   private static final String MIME_TYPE = "video/avc";
   private static final int FRAME_RATE = 30;
   private static final int IFRAME_INTERVAL = 1;
   private static final int BIT_RATE = 6000000;
   private static final int TIMEOUT_US = 10000;
   
   private MediaCodec mMediaCodec;
   
   private void prepareEncoder() {
       MediaFormat format = MediaFormat.createVideoFormat(MIME_TYPE, width, height);
       format.setInteger(MediaFormat.KEY_COLOR_FORMAT, MediaCodecInfo.CodecCapabilities.COLOR_FormatSurface);
       format.setInteger(MediaFormat.KEY_BIT_RATE, BIT_RATE);
       format.setInteger(MediaFormat.KEY_FRAME_RATE, FRAME_RATE);
       format.setInteger(MediaFormat.KEY_I_FRAME_INTERVAL, IFRAME_INTERVAL);
   
       try {
           mMediaCodec = MediaCodec.createEncoderByType(MIME_TYPE);
           mMediaCodec.configure(format, null, null, MediaCodec.CONFIGURE_FLAG_ENCODE);
           Surface surface = mMediaCodec.createInputSurface();
           mMediaCodec.start();
       } catch (IOException e) {
           e.printStackTrace();
       }
   }
   

3. 将MediaProjection的输出Surface与MediaCodec的输入Surface进行连接：

   private Surface mInputSurface;
   
   private void startScreenCapture() {
       prepareEncoder();
   
       mInputSurface = mMediaCodec.createInputSurface();
       VirtualDisplay virtualDisplay = mMediaProjection.createVirtualDisplay("ScreenCapture",
               width, height, dpi, DisplayManager.VIRTUAL_DISPLAY_FLAG_PUBLIC, mInputSurface, null, null);
   }
   

4. 获取编码后的数据：

   private void drainEncoder() {
       ByteBuffer[] outputBuffers = mMediaCodec.getOutputBuffers();
       while (true) {
           int index = mMediaCodec.dequeueOutputBuffer(bufferInfo, TIMEOUT_US);
           if (index >= 0) {
               ByteBuffer outputBuffer = outputBuffers[index];
               // 处理编码后的数据
               // ...
               mMediaCodec.releaseOutputBuffer(index, false);
           } else if (index == MediaCodec.INFO_OUTPUT_FORMAT_CHANGED) {
               MediaFormat newFormat = mMediaCodec.getOutputFormat();
               // 处理编码格式变化
               // ...
           } else if (index == MediaCodec.INFO_TRY_AGAIN_LATER) {
               // 无可用输出缓冲区，等待一段时间
               break;
           }
       }
   }
   

请注意，上述代码仅提供了一种基本的实现方式，实际使用时可能需要根据具体需求进行适当调整和优化。