Services on Matrix to transform and project 3D coordinates

Redefined classes

redef class Matrix

matrix :: projection $ Matrix

A rectangular array of Float
redef class Sys

matrix :: projection $ Sys

The main class of the program.

All class definitions

redef class Matrix

matrix :: projection $ Matrix

A rectangular array of Float
redef class Sys

matrix :: projection $ Sys

The main class of the program.
package_diagram matrix::projection projection matrix matrix matrix::projection->matrix core core matrix->core ...core ... ...core->core gamnit::cameras cameras gamnit::cameras->matrix::projection gamnit::cameras_cache cameras_cache gamnit::cameras_cache->gamnit::cameras gamnit::camera_control camera_control gamnit::camera_control->gamnit::cameras gamnit::cameras_cache... ... gamnit::cameras_cache...->gamnit::cameras_cache gamnit::camera_control... ... gamnit::camera_control...->gamnit::camera_control


module abstract_collection

core :: abstract_collection

Abstract collection classes and services.
module abstract_text

core :: abstract_text

Abstract class for manipulation of sequences of characters
module array

core :: array

This module introduces the standard array structure.
module bitset

core :: bitset

Services to handle BitSet
module bytes

core :: bytes

Services for byte streams and arrays
module circular_array

core :: circular_array

Efficient data structure to access both end of the sequence.
module codec_base

core :: codec_base

Base for codecs to use with streams
module codecs

core :: codecs

Group module for all codec-related manipulations
module collection

core :: collection

This module define several collection classes.
module core

core :: core

Standard classes and methods used by default by Nit programs and libraries.
module environ

core :: environ

Access to the environment variables of the process
module error

core :: error

Standard error-management infrastructure.
module exec

core :: exec

Invocation and management of operating system sub-processes.
module file

core :: file

File manipulations (create, read, write, etc.)
module fixed_ints

core :: fixed_ints

Basic integers of fixed-precision
module fixed_ints_text

core :: fixed_ints_text

Text services to complement fixed_ints
module flat

core :: flat

All the array-based text representations
module gc

core :: gc

Access to the Nit internal garbage collection mechanism
module hash_collection

core :: hash_collection

Introduce HashMap and HashSet.
module iso8859_1

core :: iso8859_1

Codec for ISO8859-1 I/O
module kernel

core :: kernel

Most basic classes and methods.
module list

core :: list

This module handle double linked lists
module math

core :: math

Mathematical operations
module native

core :: native

Native structures for text and bytes
module numeric

core :: numeric

Advanced services for Numeric types
module protocol

core :: protocol

module queue

core :: queue

Queuing data structures and wrappers
module range

core :: range

Module for range of discrete objects.
module re

core :: re

Regular expression support for all services based on Pattern
module ropes

core :: ropes

Tree-based representation of a String.
module sorter

core :: sorter

This module contains classes used to compare things and sorts arrays.
module stream

core :: stream

Input and output streams of characters
module text

core :: text

All the classes and methods related to the manipulation of text entities
module time

core :: time

Management of time and dates
module union_find

core :: union_find

union–find algorithm using an efficient disjoint-set data structure
module utf8

core :: utf8

Codec for UTF-8 I/O


module matrix

matrix :: matrix

Services for matrices of Float values


module cameras

gamnit :: cameras

Camera services producing Model-View-Projection matrices


module a_star-m


module bmfont

gamnit :: bmfont

Parse Angel Code BMFont format and draw text
module camera_control

gamnit :: camera_control

Simple camera control for user, as the method accept_scroll_and_zoom
module camera_control_android

gamnit :: camera_control_android

Two fingers camera manipulation, pinch to zoom and slide to scroll
module camera_control_linux

gamnit :: camera_control_linux

Mouse wheel and middle mouse button to control camera
module cameras_cache

gamnit :: cameras_cache

Cache the Matrix produced by Camera::mvp_matrix
module cardboard

gamnit :: cardboard

Update the orientation of world_camera at each frame using the head position given by android::cardboard
module depth

gamnit :: depth

Framework for 3D games in Nit
module depth_core

gamnit :: depth_core

Base entities of the depth 3D game framework
module flat

gamnit :: flat

Simple API for 2D games, built around Sprite and App::update
module flat_core

gamnit :: flat_core

Core services for the flat API for 2D games
module font

gamnit :: font

Abstract font drawing services, implemented by bmfont and tileset
module model_dimensions

gamnit :: model_dimensions

Dimensions related services for Model and Mesh
module more_lights

gamnit :: more_lights

More implementations of Light
module more_materials

gamnit :: more_materials

Various material implementations
module more_meshes

gamnit :: more_meshes

More simple geometric meshes
module more_models

gamnit :: more_models

Services to load models from the assets folder
module particles

gamnit :: particles

Particle effects
module selection

gamnit :: selection

Select Actor from a screen coordinate
module shadow

gamnit :: shadow

Shadow mapping using a depth texture
module stereoscopic_view

gamnit :: stereoscopic_view

Refine EulerCamera and App::frame_core_draw to get a stereoscopic view
module tileset

gamnit :: tileset

Support for TileSet, TileSetFont and drawing text with TextSprites
module virtual_gamepad

gamnit :: virtual_gamepad

Virtual gamepad mapped to keyboard keys for quick and dirty mobile support
module vr

gamnit :: vr

VR support for gamnit depth, for Android only
# Services on `Matrix` to transform and project 3D coordinates
module projection

intrude import matrix

redef class Matrix

	# Create an orthogonal projection matrix
	# `left, right, bottom, top, near, far` defines the world clip planes.
	new orthogonal(left, right, bottom, top, near, far: Float)
		var dx = right - left
		var dy = top - bottom
		var dz = far - near

		assert dx != 0.0 and dy != 0.0 and dz != 0.0

		var mat = new Matrix.identity(4)
		mat[0, 0] = 2.0 / dx
		mat[3, 0] = -(right + left) / dx
		mat[1, 1] = 2.0 / dy
		mat[3, 1] = -(top + bottom) / dy
		mat[2, 2] = 2.0 / dz
		mat[3, 2] = -(near + far) / dz
		return mat

	# Create a perspective transformation matrix
	# Using the given vertical `field_of_view_y` in radians, the `aspect_ratio`
	# and the `near`/`far` world distances.
	new perspective(field_of_view_y, aspect_ratio, near, far: Float)
		var frustum_height = (field_of_view_y/2.0).tan * near
		var frustum_width = frustum_height * aspect_ratio

		return new Matrix.frustum(-frustum_width, frustum_width,
		                          -frustum_height, frustum_height,
		                          near, far)

	# Create a frustum transformation matrix
	# `left, right, bottom, top, near, far` defines the world clip planes.
	new frustum(left, right, bottom, top, near, far: Float)
		var dx = right - left
		var dy = top - bottom
		var dz = far - near

		assert near > 0.0
		assert far > 0.0
		assert dx > 0.0
		assert dy > 0.0
		assert dz > 0.0

		var mat = new Matrix(4, 4)

		mat[0, 0] = 2.0 * near / dx
		mat[0, 1] = 0.0
		mat[0, 2] = 0.0
		mat[0, 3] = 0.0

		mat[1, 0] = 0.0
		mat[1, 1] = 2.0 * near / dy
		mat[1, 2] = 0.0
		mat[1, 3] = 0.0

		mat[2, 0] = (right + left) / dx
		mat[2, 1] = (top + bottom) / dy
		mat[2, 2] = -(near + far) / dz
		mat[2, 3] = -1.0

		mat[3, 0] = 0.0
		mat[3, 1] = 0.0
		mat[3, 2] = -2.0 * near * far / dz
		mat[3, 3] = 0.0

		return mat

	# Apply a translation by `x, y, z` to this matrix
	fun translate(x, y, z: Float)
		for i in [0..3] do
			self[3, i] = self[3,i] + self[0, i] * x + self[1, i] * y + self[2, i] * z

	# Apply scaling on `x, y, z` to this matrix
	fun scale(x, y, z: Float)
		for i in [0..3] do
			self[0, i] = self[0, i] * x
			self[1, i] = self[1, i] * y
			self[2, i] = self[2, i] * z

	# Create a rotation matrix by `angle` around the vector defined by `x, y, z`
	new rotation(angle, x, y, z: Float)
		var mat = new Matrix.identity(4)

		var mag = (x*x + y*y + z*z).sqrt
		var sin = angle.sin
		var cos = angle.cos

		if mag > 0.0 then
			x = x / mag
			y = y / mag
			z = z / mag

			var inv_cos = 1.0 - cos

			mat[0, 0] = inv_cos*x*x + cos
			mat[0, 1] = inv_cos*x*y - z*sin
			mat[0, 2] = inv_cos*z*x + y*sin

			mat[1, 0] = inv_cos*x*y + z*sin
			mat[1, 1] = inv_cos*y*y + cos
			mat[1, 2] = inv_cos*y*z - x*sin

			mat[2, 0] = inv_cos*z*x - y*sin
			mat[2, 1] = inv_cos*y*z + x*sin
			mat[2, 2] = inv_cos*z*z + cos
		return mat

	# Apply a rotation of `angle` radians around the vector `x, y, z`
	fun rotate(angle, x, y, z: Float)
		var rotation = new Matrix.rotation(angle, x, y, z)
		var rotated = self * rotation
		self.items = rotated.items

	# Rotation matrix from Euler angles `pitch`, `yaw` and `roll` in radians
	# Apply a composition of intrinsic rotations around the axes x-y'-z''.
	# Or `pitch` around the X axis, `yaw` around Y and `roll` around Z,
	# applied successively. All rotations follow the right hand rule.
	# This service aims to respect the world axes and logic of `gamnit`,
	# it may not correspond to all needs.
	# The returned `Matrix` may be cached, it must not be modified.
	new gamnit_euler_rotation(pitch, yaw, roll: Float)
		if pitch == 0.0 and yaw == 0.0 and roll == 0.0 then
			return once new Matrix.identity(4)

		if rotation_pitch == pitch and rotation_yaw == yaw and rotation_roll == roll then
			var rot = rotation_matrix_cache
			if rot != null then return rot

		var c1 = pitch.cos
		var s1 = pitch.sin
		var c2 = yaw.cos
		var s2 = yaw.sin
		var c3 = roll.cos
		var s3 = roll.sin

		var rot = new Matrix(4, 4)
			          c2*c3,          -c2*s3,   -s2, 0.0,
			 c1*s3+c3*s1*s2,  c1*c3-s1*s2*s3, c2*s1, 0.0,
			-s1*s3+c1*c3*s2, -c3*s1-c1*s2*s3, c1*c2, 0.0,
			            0.0,             0.0,   0.0, 1.0)

		rotation_matrix_cache = rot
		rotation_pitch = pitch
		rotation_yaw = yaw
		rotation_roll = roll
		return rot

redef class NativeDoubleArray
	fun mat4_set(f0, f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12, f13, f14, f15: Float) `{
		self[ 0] =  f0;
		self[ 1] =  f1;
		self[ 2] =  f2;
		self[ 3] =  f3;

		self[ 4] =  f4;
		self[ 5] =  f5;
		self[ 6] =  f6;
		self[ 7] =  f7;

		self[ 8] =  f8;
		self[ 9] =  f9;
		self[10] = f10;
		self[11] = f11;

		self[12] = f12;
		self[13] = f13;
		self[14] = f14;
		self[15] = f15;

redef class Sys

	private var rotation_matrix_cache: nullable Matrix = null
	private var rotation_pitch = 0.0
	private var rotation_yaw = 0.0
	private var rotation_roll = 0.0