Adding a 3d Perspective and Object Rendering to Our Air Hockey Project in Native C Code

Posted on September 18, 2013 by Kevin

For this post in the air hockey series, we’ll learn how to render our scene from a 3D perspective, as well as how to add a puck and two mallets to the scene. We’ll also see how easy it is to bring these changes to Android, iOS, and emscripten.

Prerequisites

This lesson continues the air hockey project series, building upon the code from GitHub for ‘article-2-loading-png-file’. Here are the previous posts in this series:

Setting up a simple build system

Adding support for PNG loading into a texture

Adding support for a matrix library

The first thing we’ll do is add support for a matrix library so we can use the same matrix math on all three platforms, and then we’ll introduce the changes to our code from the top down. There are a lot of libraries out there, so I decided to use linmath.h by Wolfgang Draxinger for its simplicity and compactness. Since it’s on GitHub, we can easily add it to our project by running the following git command from the root airhockey/ folder:

git submodule add https://github.com/datenwolf/linmath.h.git src/3rdparty/linmath

Updating our game code

We’ll introduce all of the changes from the top down, so let’s begin by replacing everything inside game.c as follows:

Headers and declarations

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#include "game.h"
#include "game_objects.h"
#include "asset_utils.h"
#include "buffer.h"
#include "image.h"
#include "linmath.h"
#include "math_helper.h"
#include "matrix.h"
#include "platform_gl.h"
#include "platform_asset_utils.h"
#include "program.h"
#include "shader.h"
#include "texture.h"

static const float puck_height = 0.02f;
static const float mallet_height = 0.15f;

static Table table;
static Puck puck;
static Mallet red_mallet;
static Mallet blue_mallet;

static TextureProgram texture_program;
static ColorProgram color_program;

static mat4x4 projection_matrix;
static mat4x4 model_matrix;
static mat4x4 view_matrix;

static mat4x4 view_projection_matrix;
static mat4x4 model_view_projection_matrix;

static void position_table_in_scene();
static void position_object_in_scene(float x, float y, float z);

We’ve added all of the new includes, constants, variables, and function declarations that we’ll need for our new game code. We’ll use Table, Puck, and Mallet to represent our drawable objects, TextureProgram and ColorProgram to represent our shader programs, and the mat4x4 (a datatype from linmath.h) matrices for our OpenGL matrices. In our draw loop, we’ll call position_table_in_scene() to position the table, and position_object_in_scene() to position our other objects.

For those of you who have also followed the Java tutorials from OpenGL ES 2 for Android: A Quick-Start Guide, you’ll recognize that this has a lot in common with the air hockey project from the first part of the book. The code for that project can be freely downloaded from The Pragmatic Bookshelf.

`on_surface_created()`

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void on_surface_created() {
    glClearColor(0.0f, 0.0f, 0.0f, 0.0f);
    glEnable(GL_DEPTH_TEST);

    table = create_table(
        load_png_asset_into_texture("textures/air_hockey_surface.png"));

    vec4 puck_color = {0.8f, 0.8f, 1.0f, 1.0f};
    vec4 red = {1.0f, 0.0f, 0.0f, 1.0f};
    vec4 blue = {0.0f, 0.0f, 1.0f, 1.0f};

    puck = create_puck(0.06f, puck_height, 32, puck_color);
    red_mallet = create_mallet(0.08f, mallet_height, 32, red);
    blue_mallet = create_mallet(0.08f, mallet_height, 32, blue);

    texture_program = get_texture_program(build_program_from_assets(
        "shaders/texture_shader.vsh", "shaders/texture_shader.fsh"));
    color_program = get_color_program(build_program_from_assets(
        "shaders/color_shader.vsh", "shaders/color_shader.fsh"));
}

Our new on_surface_created() enables depth-testing, initializes the table, puck, and mallets, and loads in the shader programs.

`on_surface_changed(int width, int height)`

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void on_surface_changed(int width, int height) {
    glViewport(0, 0, width, height);
    mat4x4_perspective(projection_matrix, 45, (float) width / (float) height, 1, 10);
    mat4x4_look_at(view_matrix, 0.0f, 1.2f, 2.2f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f);
}

Our new on_surface_changed(int width, int height) now takes in two parameters for the width and the height, and it sets up a projection matrix, and then sets up the view matrix to be slightly above and behind the origin, with an eye position of (0, 1.2, 2.2).

`on_draw_frame()`

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void on_draw_frame() {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
    mat4x4_mul(view_projection_matrix, projection_matrix, view_matrix);

    position_table_in_scene();
    draw_table(&table, &texture_program, model_view_projection_matrix);

    position_object_in_scene(0.0f, mallet_height / 2.0f, -0.4f);
    draw_mallet(&red_mallet, &color_program, model_view_projection_matrix);

    position_object_in_scene(0.0f, mallet_height / 2.0f, 0.4f);
    draw_mallet(&blue_mallet, &color_program, model_view_projection_matrix);

    // Draw the puck.
    position_object_in_scene(0.0f, puck_height / 2.0f, 0.0f);
    draw_puck(&puck, &color_program, model_view_projection_matrix);
}

Our new on_draw_frame() positions and draws the table, mallets, and the puck.

Because we changed the definition of on_surface_changed(), we also have to change the declaration in game.h. Change void on_surface_changed(); to void on_surface_changed(int width, int height);.

Adding new helper functions

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static void position_table_in_scene() {
    // The table is defined in terms of X & Y coordinates, so we rotate it
    // 90 degrees to lie flat on the XZ plane.
    mat4x4 rotated_model_matrix;
    mat4x4_identity(model_matrix);
    mat4x4_rotate_X(rotated_model_matrix, model_matrix, deg_to_radf(-90.0f));
    mat4x4_mul(
        model_view_projection_matrix, view_projection_matrix, rotated_model_matrix);
}

static void position_object_in_scene(float x, float y, float z) {
    mat4x4_identity(model_matrix);
    mat4x4_translate_in_place(model_matrix, x, y, z);
    mat4x4_mul(model_view_projection_matrix, view_projection_matrix, model_matrix);
}

These functions update the matrices to let us position the table, puck, and mallets in the scene. We’ll define all of the extra functions that we need soon.

Adding new shaders

Now we’ll start drilling down into each part of the program and make the changes necessary for our game code to work. Let’s begin by updating our shaders. First, let’s rename our vertex shader shader.vsh to texture_shader.vsh and update it as follows:

texture_shader.vsh

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uniform mat4 u_MvpMatrix;

attribute vec4 a_Position;
attribute vec2 a_TextureCoordinates;

varying vec2 v_TextureCoordinates;

void main()
{
    v_TextureCoordinates = a_TextureCoordinates;
    gl_Position = u_MvpMatrix * a_Position;
}

We can rename our fragment shader shader.fsh to texture_shader.fsh without making any other changes.

We’ll also need a new set of shaders to render our puck and mallets. Let’s add the following new shaders:

color_shader.vsh

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uniform mat4 u_MvpMatrix;
attribute vec4 a_Position;
void main()
{
    gl_Position = u_MvpMatrix * a_Position;
}

color_shader.fsh

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precision mediump float;
uniform vec4 u_Color;
void main()
{
    gl_FragColor = u_Color;
}

Creating our game objects

Now we’ll add support for generating and drawing our game objects. Let’s begin with game_objects.h:

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#include "platform_gl.h"
#include "program.h"
#include "linmath.h"

typedef struct {
    GLuint texture;
    GLuint buffer;
} Table;

typedef struct {
    vec4 color;
    GLuint buffer;
    int num_points;
} Puck;

typedef struct {
    vec4 color;
    GLuint buffer;
    int num_points;
} Mallet;

Table create_table(GLuint texture);
void draw_table(const Table* table, const TextureProgram* texture_program, mat4x4 m);

Puck create_puck(float radius, float height, int num_points, vec4 color);
void draw_puck(const Puck* puck, const ColorProgram* color_program, mat4x4 m);

Mallet create_mallet(float radius, float height, int num_points, vec4 color);
void draw_mallet(const Mallet* mallet, const ColorProgram* color_program, mat4x4 m);

We’ve defined three C structs to hold the data for our table, puck, and mallets, and we’ve declared functions to create and draw these objects.

Drawing a table

Let’s continue with game_objects.c:

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#include "game_objects.h"
#include "buffer.h"
#include "platform_gl.h"
#include "program.h"
#include "linmath.h"
#include <math.h>

// Triangle fan
// position X, Y, texture S, T
static const float table_data[] = { 0.0f,  0.0f, 0.5f, 0.5f,
                                   -0.5f, -0.8f, 0.0f, 0.9f,
                                    0.5f, -0.8f, 1.0f, 0.9f,
                                    0.5f,  0.8f, 1.0f, 0.1f,
                                   -0.5f,  0.8f, 0.0f, 0.1f,
                                   -0.5f, -0.8f, 0.0f, 0.9f};

Table create_table(GLuint texture) {
    return (Table) {texture, 
        create_vbo(sizeof(table_data), table_data, GL_STATIC_DRAW)};
}

void draw_table(const Table* table, const TextureProgram* texture_program, mat4x4 m)
{
    glUseProgram(texture_program->program);

    glActiveTexture(GL_TEXTURE0);
    glBindTexture(GL_TEXTURE_2D, table->texture);
    glUniformMatrix4fv(texture_program->u_mvp_matrix_location, 1, 
        GL_FALSE, (GLfloat*)m);
    glUniform1i(texture_program->u_texture_unit_location, 0);

    glBindBuffer(GL_ARRAY_BUFFER, table->buffer);
    glVertexAttribPointer(texture_program->a_position_location, 2, GL_FLOAT,
        GL_FALSE, 4 * sizeof(GL_FLOAT), BUFFER_OFFSET(0));
    glVertexAttribPointer(texture_program->a_texture_coordinates_location, 2, GL_FLOAT,
        GL_FALSE, 4 * sizeof(GL_FLOAT), BUFFER_OFFSET(2 * sizeof(GL_FLOAT)));
    glEnableVertexAttribArray(texture_program->a_position_location);
    glEnableVertexAttribArray(texture_program->a_texture_coordinates_location);
    glDrawArrays(GL_TRIANGLE_FAN, 0, 6);

    glBindBuffer(GL_ARRAY_BUFFER, 0);
}

After the imports, this is the code to create and draw the table data. This is essentially the same as what we had before, with the coordinates adjusted a bit to change the table into a rectangle.

Generating circles and cylinders

Before we can draw a puck or a mallet, we’ll need to add some helper functions to draw a circle or a cylinder. Let’s define those now:

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static inline int size_of_circle_in_vertices(int num_points) {
    return 1 + (num_points + 1);
}

static inline int size_of_open_cylinder_in_vertices(int num_points) {
    return (num_points + 1) * 2;
}

We first need two helper functions to calculate the size of a circle or a cylinder in terms of vertices. A circle drawn as a triangle fan has one vertex for the center, num_points vertices around the circle, and one more vertex to close the circle. An open-ended cylinder drawn as a triangle strip doesn’t have a center point, but it does have two vertices for each point around the circle, and two more vertices to close off the circle.

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static inline int gen_circle(float* out, int offset, 
    float center_x, float center_y, float center_z, 
    float radius, int num_points)
{
    out[offset++] = center_x;
    out[offset++] = center_y;
    out[offset++] = center_z;

    int i;
    for (i = 0; i <= num_points; ++i) {
        float angle_in_radians = ((float) i / (float) num_points) 
                               * ((float) M_PI * 2.0f);
        out[offset++] = center_x + radius * cos(angle_in_radians);
        out[offset++] = center_y;
        out[offset++] = center_z + radius * sin(angle_in_radians);
    }

    return offset;
}

This code will generate a circle, given a center point, a radius, and the number of points around the circle.

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static inline int gen_cylinder(float* out, int offset, 
    float center_x, float center_y, float center_z, 
    float height, float radius, int num_points)
{
    const float y_start = center_y - (height / 2.0f);
    const float y_end = center_y + (height / 2.0f);

    int i;
    for (i = 0; i <= num_points; i++) {
        float angle_in_radians = ((float) i / (float) num_points) 
                               * ((float) M_PI * 2.0f);

        float x_position = center_x + radius * cos(angle_in_radians);
        float z_position = center_z + radius * sin(angle_in_radians);

        out[offset++] = x_position;
        out[offset++] = y_start;
        out[offset++] = z_position;

        out[offset++] = x_position;
        out[offset++] = y_end;
        out[offset++] = z_position;
    }

    return offset;
}

This code will generate the vertices for an open-ended cylinder. Note that for both the circle and the cylinder, the loop goes from 0 to num_points, so the first and last points around the circle are duplicated in order to close the loop around the circle.

Drawing a puck

Let’s add the code to generate and draw the puck:

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Puck create_puck(float radius, float height, int num_points, vec4 color)
{
    float data[(size_of_circle_in_vertices(num_points) 
              + size_of_open_cylinder_in_vertices(num_points)) * 3];

    int offset = gen_circle(data, 0, 0.0f, height / 2.0f, 0.0f, radius, num_points);
    gen_cylinder(data, offset, 0.0f, 0.0f, 0.0f, height, radius, num_points);

    return (Puck) {{color[0], color[1], color[2], color[3]},
                   create_vbo(sizeof(data), data, GL_STATIC_DRAW),
                   num_points};
}

A puck contains one open-ended cylinder, and a circle to top off that cylinder.

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void draw_puck(const Puck* puck, const ColorProgram* color_program, mat4x4 m)
{
    glUseProgram(color_program->program);

    glUniformMatrix4fv(color_program->u_mvp_matrix_location, 1, GL_FALSE, (GLfloat*)m);
    glUniform4fv(color_program->u_color_location, 1, puck->color);

    glBindBuffer(GL_ARRAY_BUFFER, puck->buffer);
    glVertexAttribPointer(color_program->a_position_location, 3, GL_FLOAT, 
        GL_FALSE, 0, BUFFER_OFFSET(0));
    glEnableVertexAttribArray(color_program->a_position_location);

    int circle_vertex_count = size_of_circle_in_vertices(puck->num_points);
    int cylinder_vertex_count = size_of_open_cylinder_in_vertices(puck->num_points);

    glDrawArrays(GL_TRIANGLE_FAN, 0, circle_vertex_count);
    glDrawArrays(GL_TRIANGLE_STRIP, circle_vertex_count, cylinder_vertex_count);
    glBindBuffer(GL_ARRAY_BUFFER, 0);
}

To draw the puck, we pass in the uniforms and attributes, and then we draw the circle as a triangle fan, and the cylinder as a triangle strip.

Drawing a mallet

Let’s continue with the code to create and draw a mallet:

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Mallet create_mallet(float radius, float height, int num_points, vec4 color)
{
    float data[(size_of_circle_in_vertices(num_points) * 2 
              + size_of_open_cylinder_in_vertices(num_points) * 2) * 3];

    float base_height = height * 0.25f;
    float handle_height = height * 0.75f;
    float handle_radius = radius / 3.0f;

    int offset = gen_circle(data, 0, 0.0f, -base_height, 0.0f, radius, num_points);
    offset = gen_circle(data, offset, 
        0.0f, height * 0.5f, 0.0f, 
        handle_radius, num_points);
    offset = gen_cylinder(data, offset, 
        0.0f, -base_height - base_height / 2.0f, 0.0f, 
        base_height, radius, num_points);
    gen_cylinder(data, offset, 
        0.0f, height * 0.5f - handle_height / 2.0f, 0.0f, 
        handle_height, handle_radius, num_points);

    return (Mallet) {{color[0], color[1], color[2], color[3]},
                     create_vbo(sizeof(data), data, GL_STATIC_DRAW),
                     num_points};
}

A mallet contains two circles and two open-ended cylinders, positioned and sized so that the mallet’s base is wider and shorter than the mallet’s handle.

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void draw_mallet(const Mallet* mallet, const ColorProgram* color_program, mat4x4 m)
{
    glUseProgram(color_program->program);

    glUniformMatrix4fv(color_program->u_mvp_matrix_location, 1, GL_FALSE, (GLfloat*)m);
    glUniform4fv(color_program->u_color_location, 1, mallet->color);

    glBindBuffer(GL_ARRAY_BUFFER, mallet->buffer);
    glVertexAttribPointer(color_program->a_position_location, 3, GL_FLOAT, 
    GL_FALSE, 0, BUFFER_OFFSET(0));
    glEnableVertexAttribArray(color_program->a_position_location);

    int circle_vertex_count = size_of_circle_in_vertices(mallet->num_points);
    int cylinder_vertex_count = size_of_open_cylinder_in_vertices(mallet->num_points);
    int start_vertex = 0;

    glDrawArrays(GL_TRIANGLE_FAN, start_vertex, circle_vertex_count); 
    start_vertex += circle_vertex_count;
    glDrawArrays(GL_TRIANGLE_FAN, start_vertex, circle_vertex_count); 
    start_vertex += circle_vertex_count;
    glDrawArrays(GL_TRIANGLE_STRIP, start_vertex, cylinder_vertex_count); 
    start_vertex += cylinder_vertex_count;
    glDrawArrays(GL_TRIANGLE_STRIP, start_vertex, cylinder_vertex_count);
    glBindBuffer(GL_ARRAY_BUFFER, 0);
}

Drawing the mallet is similar to drawing the puck, except that now we draw two circles and two cylinders.

Adding math helper functions

We’ll need to add a helper function that we’re currently using in game.c; create a new header file called math_helper.h, and add the following code:

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#include <math.h>

static inline float deg_to_radf(float deg) {
    return deg * (float)M_PI / 180.0f;
}

Since C’s trigonometric functions expect passed-in values to be in radians, we’ll use this function to convert degrees into radians, where needed.

Adding matrix helper functions

While linmath.h contains a lot of useful functions, there’s a few missing that we need for our game code. Create a new header file called matrix.h, and begin by adding the following code, all adapted from Android’s OpenGL Matrix class:

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#include "linmath.h"
#include <math.h>
#include <string.h>

/* Adapted from Android's OpenGL Matrix.java. */

static inline void mat4x4_perspective(mat4x4 m, float y_fov_in_degrees, 
    float aspect, float n, float f)
{
    const float angle_in_radians = (float) (y_fov_in_degrees * M_PI / 180.0);
    const float a = (float) (1.0 / tan(angle_in_radians / 2.0));

    m[0][0] = a / aspect;
    m[1][0] = 0.0f;
    m[2][0] = 0.0f;
    m[3][0] = 0.0f;

    m[1][0] = 0.0f;
    m[1][1] = a;
    m[1][2] = 0.0f;
    m[1][3] = 0.0f;

    m[2][0] = 0.0f;
    m[2][1] = 0.0f;
    m[2][2] = -((f + n) / (f - n));
    m[2][3] = -1.0f;

    m[3][0] = 0.0f;
    m[3][1] = 0.0f;
    m[3][2] = -((2.0f * f * n) / (f - n));
    m[3][3] = 0.0f;
}

We’ll use mat4x4_perspective() to setup a perspective projection matrix.

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static inline void mat4x4_translate_in_place(mat4x4 m, float x, float y, float z)
{
    int i;
    for (i = 0; i < 4; ++i) {
        m[3][i] += m[0][i] * x
                +  m[1][i] * y
                +  m[2][i] * z;
    }
}

This helper function lets us translate a matrix in place.

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static inline void mat4x4_look_at(mat4x4 m,
        float eyeX, float eyeY, float eyeZ,
        float centerX, float centerY, float centerZ,
        float upX, float upY, float upZ)
{
    // See the OpenGL GLUT documentation for gluLookAt for a description
    // of the algorithm. We implement it in a straightforward way:

    float fx = centerX - eyeX;
    float fy = centerY - eyeY;
    float fz = centerZ - eyeZ;

    // Normalize f
    vec3 f_vec = {fx, fy, fz};
    float rlf = 1.0f / vec3_len(f_vec);
    fx *= rlf;
    fy *= rlf;
    fz *= rlf;

    // compute s = f x up (x means "cross product")
    float sx = fy * upZ - fz * upY;
    float sy = fz * upX - fx * upZ;
    float sz = fx * upY - fy * upX;

    // and normalize s
    vec3 s_vec = {sx, sy, sz};
    float rls = 1.0f / vec3_len(s_vec);
    sx *= rls;
    sy *= rls;
    sz *= rls;

    // compute u = s x f
    float ux = sy * fz - sz * fy;
    float uy = sz * fx - sx * fz;
    float uz = sx * fy - sy * fx;

    m[0][0] = sx;
    m[0][1] = ux;
    m[0][2] = -fx;
    m[0][3] = 0.0f;

    m[1][0] = sy;
    m[1][1] = uy;
    m[1][2] = -fy;
    m[1][3] = 0.0f;

    m[2][0] = sz;
    m[2][1] = uz;
    m[2][2] = -fz;
    m[2][3] = 0.0f;

    m[3][0] = 0.0f;
    m[3][1] = 0.0f;
    m[3][2] = 0.0f;
    m[3][3] = 1.0f;

    mat4x4_translate_in_place(m, -eyeX, -eyeY, -eyeZ);
}

We can use mat4x4_look_at() like a camera, and use it to position the scene in a certain way.

Adding shader program wrappers

We’re almost done the changes to our core code. Let’s wrap up those changes by adding the following code:

program.h

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#pragma once
#include "platform_gl.h"

typedef struct {
    GLuint program;

    GLint a_position_location;
    GLint a_texture_coordinates_location;
    GLint u_mvp_matrix_location;
    GLint u_texture_unit_location;
} TextureProgram;

typedef struct {
    GLuint program;

    GLint a_position_location;
    GLint u_mvp_matrix_location;
    GLint u_color_location;
} ColorProgram;

TextureProgram get_texture_program(GLuint program);
ColorProgram get_color_program(GLuint program);

program.c

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#include "program.h"
#include "platform_gl.h"

TextureProgram get_texture_program(GLuint program)
{
    return (TextureProgram) {
            program,
            glGetAttribLocation(program, "a_Position"),
            glGetAttribLocation(program, "a_TextureCoordinates"),
            glGetUniformLocation(program, "u_MvpMatrix"),
            glGetUniformLocation(program, "u_TextureUnit")};
}

ColorProgram get_color_program(GLuint program)
{
    return (ColorProgram) {
            program,
            glGetAttribLocation(program, "a_Position"),
            glGetUniformLocation(program, "u_MvpMatrix"),
            glGetUniformLocation(program, "u_Color")};
}

Adding support for Android

We first need to update Android.mk and add the following to LOCAL_SRC_FILES:

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$(CORE_RELATIVE_PATH)/game_objects.c \
$(CORE_RELATIVE_PATH)/program.c \

We also need to add a new LOCAL_C_INCLUDES:

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LOCAL_C_INCLUDES += $(PROJECT_ROOT_PATH)/3rdparty/linmath/

We then need to update renderer_wrapper.c and change the call to on_surface_changed(); to on_surface_changed(width, height);. Once we’ve done that, we should be able to run the app on our Android device, and it should look similar to the following image:

Adding support for iOS

For iOS, we just need to open up the Xcode project and add the necessary references to linmath.h and our new core files to the appropriate folder groups, and then we need to update ViewController.m and change on_surface_changed(); to the following:

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on_surface_changed([[self view] bounds].size.width, [[self view] bounds].size.height);

Once we run the app, it should look similar to the following image:

Air hockey, running on the iPhone simulator

Adding support for emscripten

For emscripten, we need to update the Makefile and add the following lines to SOURCES:

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../../core/game_objects.c \
../../core/program.c \

We’ll also need to add the following lines to OBJECTS:

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../../core/game_objects.o \
../../core/program.o \

We then just need to update main.c, move the constants width and height from inside init_gl() to outside the function near the top of the file, and update the call to on_surface_changed(); to on_surface_changed(width, height);. We can then build the file by calling emmake make, which should produce a file that looks as follows:

See how easy that was? Now that we have a minimal cross-platform framework in place, it’s very easy for us to bring changes to the core code across to each platform.

Exploring further

The full source code for this lesson can be found at the GitHub project. In the next post, we’ll take a look at user input so we can move our mallet around the screen.