V.7 V.7 - 9 months ago 98
Pascal Question

How to draw an object and rotate it in oblique frontal projection

How to draw an object and rotate it in oblique frontal (dimetric) projection properly ?

An illustration of projection:

Oblique frontal projection

I've already made a program (Pascal with Graph unit) which does it, but I think that it draws an object incorrectly.

program p7test;

uses PtcCrt, PtcGraph;

type
TPixel = record
x, y, z: real;
end;
TModel = record
p: array [ 1..8 ] of TPixel;
end;
TCenter = record
xc, zc: integer;
end;

var
Driver, Mode: integer;
c: char;
s: string;
ns, rx, ry, rz, ra, m_l, m_w, m_h, m_l_d, m_w_d, m_h_d: integer;
model_d, model: TModel;
center: TCenter;

procedure LineXYZ( sp_t, ep_t: TPixel; center_t: TCenter );
var
x1, y1, x2, y2: real;
begin
x1 := sp_t.x - sin( pi / 4 ) * sp_t.y / 2;
y1 := sp_t.z - sin( pi / 4 ) * sp_t.y / 2;
x2 := ep_t.x - sin( pi / 4 ) * ep_t.y / 2;
y2 := ep_t.z - sin( pi / 4 ) * ep_t.y / 2;
Line(
round( center_t.xc - x1 ),
round( center_t.zc - y1 ),
round( center_t.xc - x2 ),
round( center_t.zc - y2 )
);
end;

procedure DrawModel( model_t: TModel; center_t: TCenter );
var
i: integer;
begin
LineXYZ( model_t.p[ 1 ], model_t.p[ 2 ], center_t );
LineXYZ( model_t.p[ 2 ], model_t.p[ 3 ], center_t );
LineXYZ( model_t.p[ 3 ], model_t.p[ 4 ], center_t );
LineXYZ( model_t.p[ 4 ], model_t.p[ 1 ], center_t );
LineXYZ( model_t.p[ 5 ], model_t.p[ 6 ], center_t );
LineXYZ( model_t.p[ 6 ], model_t.p[ 7 ], center_t );
LineXYZ( model_t.p[ 7 ], model_t.p[ 8 ], center_t );
LineXYZ( model_t.p[ 8 ], model_t.p[ 5 ], center_t );
LineXYZ( model_t.p[ 1 ], model_t.p[ 5 ], center_t );
LineXYZ( model_t.p[ 2 ], model_t.p[ 6 ], center_t );
LineXYZ( model_t.p[ 3 ], model_t.p[ 7 ], center_t );
LineXYZ( model_t.p[ 4 ], model_t.p[ 8 ], center_t );
end;

function RotateZ( model_t: TModel; angle: real ): TModel;
var
x, y: real;
i: integer;
begin
angle := angle * pi / 180;
for i := 1 to 8 do
begin
x := model_t.p[ i ].x;
y := model_t.p[ i ].y;
model_t.p[ i ].x := x * cos( angle ) - y * sin( angle );
model_t.p[ i ].y := y * cos( angle ) + x * sin( angle );
end;
RotateZ := model_t;
end;

function RotateY( model_t: TModel; angle: real ): TModel;
var
x, z: real;
i: integer;
begin
angle := angle * pi / 180;
for i := 1 to 8 do
begin
x := model_t.p[ i ].x;
z := model_t.p[ i ].z;
model_t.p[ i ].x := x * cos( angle ) - z * sin( angle );
model_t.p[ i ].z := z * cos( angle ) + x * sin( angle );
end;
RotateY := model_t;
end;

function RotateX( model_t: TModel; angle: real ): TModel;
var
y, z: real;
i: integer;
begin
angle := angle * pi / 180;
for i := 1 to 8 do
begin
y := model_t.p[ i ].y;
z := model_t.p[ i ].z;
model_t.p[ i ].y := y * cos( angle ) - z * sin( angle );
model_t.p[ i ].z := z * cos( angle ) + y * sin( angle );
end;
RotateX := model_t;
end;

function RotateXYZ( model_t: TModel; rx_t, ry_t, rz_t: integer ): TModel;
begin
model_t := RotateX( model_t, rx_t );
model_t := RotateY( model_t, ry_t );
model_t := RotateZ( model_t, rz_t );
RotateXYZ := model_t;
end;

begin
Driver := D8bit;
Mode := m800x600;
InitGraph( Driver, Mode, '' );
ra := 2;
if ( GraphResult <> GrOk ) then WriteLn( '640x480x256''s not supported' ) else
begin
ClearDevice;
center.xc := ( GetMaxX div 2 ) + 1;
center.zc := ( GetMaxY div 2 ) + 1;
m_l_d := 200; m_w_d := 200; m_h_d := 200;
m_l := m_l_d; m_w := m_w_d; m_h := m_h_d;
rx := -26; ry := 6; rz := 16;

model_d.p[ 1 ].x := - m_l / 2; model_d.p[ 1 ].y := - m_w / 2; model_d.p[ 1 ].z := - m_h / 2;
model_d.p[ 2 ].x := - m_l / 2; model_d.p[ 2 ].y := m_w / 2; model_d.p[ 2 ].z := - m_h / 2;
model_d.p[ 3 ].x := m_l / 2; model_d.p[ 3 ].y := m_w / 2; model_d.p[ 3 ].z := - m_h / 2;
model_d.p[ 4 ].x := m_l / 2; model_d.p[ 4 ].y := - m_w / 2; model_d.p[ 4 ].z := - m_h / 2;
model_d.p[ 5 ].x := - m_l / 2; model_d.p[ 5 ].y := - m_w / 2; model_d.p[ 5 ].z := m_h / 2;
model_d.p[ 6 ].x := - m_l / 2; model_d.p[ 6 ].y := m_w / 2; model_d.p[ 6 ].z := m_h / 2;
model_d.p[ 7 ].x := m_l / 2; model_d.p[ 7 ].y := m_w / 2; model_d.p[ 7 ].z := m_h / 2;
model_d.p[ 8 ].x := m_l / 2; model_d.p[ 8 ].y := - m_w / 2; model_d.p[ 8 ].z := m_h / 2;

model := RotateXYZ( model_d, rx, ry, rz );
SetColor( 2 ); DrawModel( model, center );
SetColor( 12 );
Str( rx, s ); OutTextXY( 2, 2, 'rx=' + s );
Str( ry, s ); OutTextXY( 2, 12, 'ry=' + s );
Str( rz, s ); OutTextXY( 2, 22, 'rz=' + s );

repeat Delay( 100 ) until KeyPressed;
if ns = 0 then ns := 1 else ns := 0;
ReadKey;
repeat
c := ReadKey;
case c of
#113: begin rx := rx - ra; model := RotateXYZ( model_d, rx, ry, rz ); end;
#101: begin rx := rx + ra; model := RotateXYZ( model_d, rx, ry, rz ); end;
#119: begin ry := ry - ra; model := RotateXYZ( model_d, rx, ry, rz ); end;
#115: begin ry := ry + ra; model := RotateXYZ( model_d, rx, ry, rz ); end;
#97: begin rz := rz - ra; model := RotateXYZ( model_d, rx, ry, rz ); end;
#100: begin rz := rz + ra; model := RotateXYZ( model_d, rx, ry, rz ); end;
#117: begin
rx := 0; ry := 0; rz := 0;
model := RotateXYZ( model_d, rx, ry, rz );
end;
end;
ClearDevice;

SetColor( 2 ); DrawModel( model, center );
SetColor( 12 );
Str( rx, s ); OutTextXY( 2, 2, 'rx=' + s );
Str( ry, s ); OutTextXY( 2, 12, 'ry=' + s );
Str( rz, s ); OutTextXY( 2, 22, 'rz=' + s );

if ns = 0 then
begin
SetActivePage(0);
SetVisualPage(1)
end
else
begin
SetActivePage(1);
SetVisualPage(0)
end;
if ns = 0 then ns := 1 else ns := 0;
until c = #27;
CloseGraph;
end;
end.


You might use WASDQER keys to rotate an object.

So as you see in picture below there's some issue when you're looking at it and it's slightly elongated:

Object rotation 1

Isn't it should look like one below ?:

Object rotation 2

I've tried to change LineXYZ lines to this:

x1 := sp_t.x - ( sp_t.y / 2 );
y1 := sp_t.z - ( sp_t.y / 2 );
x2 := ep_t.x - ( ep_t.y / 2 );
y2 := ep_t.z - ( ep_t.y / 2 );


, but I think that's not right, too.




Am I rotating x, y, z coordinates with functions like ( Rotate* ) correctly ?
Btw I think that the main problem is with LineXYZ function ( y coordinate part )
How to draw an object in this type of projection ?

Thank you very much as needed.

Best regards,
V7

Answer Source

Isn't it should look like one below?

Not, gif below is 90-90 projection, while your axis are 135-90

Your code is correct, except two things:

  1. Your X axis is wrong directed
  2. You use sin instead of cos, while angle is pi/4 they're same, but if you plan to change angle...

Your code:

x1 := sp_t.x - sin( pi / 4 ) * sp_t.y / 2;
y1 := sp_t.z - sin( pi / 4 ) * sp_t.y / 2;
x2 := ep_t.x - sin( pi / 4 ) * ep_t.y / 2;
y2 := ep_t.z - sin( pi / 4 ) * ep_t.y / 2;

Should be:

x1 := -sp_t.x - cos( pi / 4 ) * sp_t.y / 2;
y1 :=  sp_t.z - sin( pi / 4 ) * sp_t.y / 2;
x2 := -ep_t.x - cos( pi / 4 ) * ep_t.y / 2;
y2 :=  ep_t.z - sin( pi / 4 ) * ep_t.y / 2;

In rest your render is correct.

Live Demo


About @lurker notes:
No reason to fix perspective illusion here (it's something personificated - impossible to compensate it for all viewers equally).

This gif just demonstrate this illusion effect:
Illusion Demonstration

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