Three-dimensional printing apparatus and three-dimensional object printing method

1. A three-dimensional printing apparatus that cures liquid photo-curable resin to sequentially stack resin layers each having a predetermined cross-sectional shape to print a three-dimensional object, the apparatus comprising:

a tank storing the liquid photo-curable resin and including a printing region in which the three-dimensional object is to be printed;

a projector to project a first image having a quadrangular or substantially quadrangular shape onto the tank; and

a controller to control the projector; wherein

the controller includes:

a matrix calculator to calculate a projective transformation matrix by which the first image is projectively transformed so that the first image is presented on an entirety of the printing region;

an acquirer to transform the first image using the projective transformation matrix, thus acquiring a second image obtained by correction of the first image, the second image including a projection sub-image having a quadrangular or substantially quadrangular shape;

an inclination calculator to calculate a horizontal inclination and a vertical inclination of the projection sub-image in the second image;

a vertical and horizontal correction value calculator to calculate, based on the horizontal inclination, a first correction value by which a horizontal brightness distribution of the first image is corrected, and to calculate, based on the vertical inclination, a second correction value by which a vertical brightness distribution of the first image is corrected;

a memory to store a third correction value by which a brightness distribution of the first image projected onto the entirety of the printing region is corrected, the first image projected having a rectangular, substantially rectangular, square or substantially square shape;

a corrector to correct a brightness distribution of the second image using a fourth correction value calculated based on the first correction value, the second correction value, and the third correction value; and

a projection controller to control the projector so that the projection sub-image of the second image whose brightness distribution has been corrected is projected from the projector onto the tank.

2. The three-dimensional printing apparatus according to claim 1 , wherein the inclination calculator includes:

a coordinate value acquirer to acquire coordinate values of four vertices of the projection sub-image in the second image, the four vertices including a first vertex, a second vertex, a third vertex, and a fourth vertex;

a horizontal inclination calculator to calculate:

coordinate values of a first intersection that is an intersection of a first vertical end of the second image and a first straight line passing through the first and second vertices;

coordinate values of a second intersection that is an intersection of the first straight line and a second vertical end of the second image;

coordinate values of a third intersection that is an intersection of the first vertical end of the second image and a second straight line passing through the third and fourth vertices;

coordinate values of a fourth intersection that is an intersection of the second straight line and the second vertical end of the second image;

a first length between the first intersection and the third intersection;

a second length between the second intersection and the fourth intersection; and

a ratio of the second length to the first length, the ratio being the horizontal inclination of the projection sub-image; and

a vertical inclination calculator to calculate:

coordinate values of a fifth intersection that is an intersection of a first horizontal end of the second image and a third straight line passing through the first and third vertices;

coordinate values of a sixth intersection that is an intersection of the third straight line and a second horizontal end of the second image;

coordinate values of a seventh intersection that is an intersection of the first horizontal end of the second image and a fourth straight line passing through the second and fourth vertices;

coordinate values of an eighth intersection that is an intersection of the fourth straight line and the second horizontal end of the second image;

a third length between the fifth intersection and the seventh intersection;

a fourth length between the sixth intersection and the eighth intersection; and

a ratio of the fourth length to the third length, the ratio being the vertical inclination of the projection sub-image.

3. The three-dimensional printing apparatus according to claim 1 , wherein the corrector normalizes the fourth correction value so that light to be applied to a darkest portion of the second image is brightest, and corrects the brightness distribution of the second image using the fourth correction value normalized.

4. The three-dimensional printing apparatus according to claim 1 , further comprising:

an image capturing device to capture an image of the tank; and

a checkered sheet disposed on the tank; wherein

the projector projects the first image onto the checkered sheet;

the image capturing device captures an image of the checkered sheet onto which the first image is projected; and

the matrix calculator calculates the projective transformation matrix using the image of the checkered sheet captured by the image capturing device.

5. The three-dimensional printing apparatus according to claim 1 , further comprising a holder disposed above the tank, the holder being lowerable such that when the holder is lowered, the holder is immersed in the photo-curable resin in the tank, the holder being raisable such that when the holder is raised, the holder lifts a portion of the photo-curable resin cured by exposure to light, wherein the projector is disposed below the tank.